exercise # 1
Question based on coulomb’s law
1 An electron at rest has a charge of 1.6 × 10–19 C. It starts moving with a velocity v = c/2, where c is the speed of light, then the new charge on it is –
(1) 1.6 × 10–19 Coulomb
(2) 1.6 × 10–19 Coulomb
(3) 1.6 × 10–19 Coulomb (4) Coulomb
2 Two similar charge of +Q , as shown in figure are placed at A and B. –q charge is placed at point C midway between A and B. –q charge will oscillate if
A c B
+Q——— q ———— +Q
(1) It is moved towards A. (2) It is moved towards B.
(3) It is moved upwards AB.
(4) Distance between A and B is reduced.
3 When the distance between two charged particle is halved, the force between them becomes –
(1) One fourth (2) One half (3) Double (4) Four times
4 Two charges are at distance (d) apart in air. Coulomb force between them is F. If a dielectric material of dielectric constant (K) is placed between them, the coulomb force now becomes.
(1) F/K (2) FK (3) F/K2 (4) K2F
5 A certain charge Q is divided at first into two parts, (q) and (Qq). Later on the charges are placed at a certain distance. If the force of interaction between the two charges is maximum then
(1) (Q/q) = (4/1) (2) (Q/q) = (2/1)
(3)(Q/q) = (3/1) (4) (Q/q) = (5/1)
6 The three charges each of 5 × 10–6 coloumb are placed at vertex of an equilateral triangle of side 10cm. The force exerted on the charge of 1 m C placed at centre of triangle in newton will be
(1) 13.5 (2) zero
(3) 4.5 (4) 6.75
7 ABC is a right angle triangle AB=3cm, BC=4cm charges + 15, +12, –12 esu are placed at A, B and C respectively. The magnitude of the force experienced by the charge at B in dyne is
(1) 125 (2) 35
(3) 22 (4) 0
8 Five point charges, each of value +q coulomb, are placed on five vertices of a regular hexagon of side L metre. The magnitude of the force on a point charge of value q coul. placed at the centre of the hexagon is –
(1) (2)
(3) (4) Zero
9 Two charged spheres A and B are charged with the charges of +10 and +20 coul. respectively and separated by a distance of 80cm. The electric field at a point on the line joining the centres of the two sphers will be zero at a distance from sphere A.
(1) 20 cm (2) 33 cm (3) 55 cm (4) 60 cm.
10 Four charges +q, +q, –q and –q are placed respectively at the corners A, B, C and D of a square of side (a), arranged in the given order. Calculate the intensity at (O) the centre of the square .
(1) (2) (3) (4)
11 The electric potential V at any point (x, y, z) in space is given by V = 4×2 volt. The electric field E in V/m at the point (1, 0, 2) is –
(1) +8 in x direction (2) 8 in –x direction (3) 16 in + x direction (4) 16 in –x direction
12 Charges of + × 10–9 are placed at each of the four corners of a square of side 8cm. The potential at the intersection of the diagonals is
(1) 150 Volt (2) 1500 Volt
(3) 900 Volt (4) 900 Volt
13 The electron potential (V) as a function of distance (x) [in meters] is given by
V = (5×2 + 10 x – 9)Volt.
The value of electric field at x =1m would be
(1) 20 Volt/m (2) 6 Volt/m (3) 11 Volt/m (4) –23 Volt/m
14 A – particle moves towards a rest nucleus, if kinetic energy of particle is 10 MeV and atomic number of nucleus is 50. The closest approach will be –
(1) 1.44 × 10–14 m (2) 2.88 × 10–14 m (3) 1.44 × 10–10 m (4) 2.88 × 10–10 m
15 A charge of Q coloumb is located at the centre of a cube. If the corner of the cube is taken as the origin, then the flux coming out from the faces of the cube in the direction of X axis will be
(1) 4 (2) Q/6 (3) Q/3 (4) Q/4
16 A rectangular surface of 2 metre width and 4 metre length, is placed in an electric field of intensity 20 newton/C, there is an angle of 60º between the perpendicular to surface and electrical field intensity. Then total flux emitted from the surface will be (In Volt metre)
(1) 80 (2) 40
(3) 20 (4) 160
17 A square of side 20cm. is enclosed by a surface of sphere of 80 cm. radius . square and sphere have the same centre. four charges +2 × 10–6 c, –5 × 10–6 c, –3 × 10–6 c, +6 × 10–6c are located at the four corners of a square, Then out going total flux from spherical surface in Nm2/c will be
(1) zero (2) (16p) × 10–6
(3) (8p) × 10–6 (4) (36 p) × 10–6
18 A charge Q is distributed over two concentric hollow spheres of radii (r) and (R) > (r) such the surface densities are equal. Find the potential at the common centre.
(1) (2)
(3) (4) none of these
19 A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of 3Q the new potential difference between the same two surfaces is
(1) V (2) 2V
(3) 4V (4) –2V
20 An electric dipole consists of two opposite charges each of magnitude 1 × 10–6 C separated by a distance 2cm. The dipole is placed in an external field of 10 × 105N/C. The maximum torque on the dipole is –
(1) 0.2 × 10–3 Nm
(2) 1.0 × 10–3 Nm
(3) 20 × 103 Nm
(4) 4 × 10–3 Nm
21 If an electric field is given by , calculate the electric flux through a surface of area 10 units lying in yz plane
(1) 100 units (2) 10 units
(3) 30 units (4) 40 units
22 Two long thin charged rods with charge density l each are placed parallel to each other at a distance d apart. The force per unit length exerted on one rod by the other will be
(1) (2)
(3) (4)
23 The electric field intensity due to a thin infinite long straight wire of uniform linear charge density l at O is –
(1) (2)
(3) (4) Zero
24 Figure shows a set of euipotential surfaces. The magnitude and direction of electric field that exists in the region is
(1) V/m at 45º with xaxis
(2) V/m at –45º with xaxis
(3) V/m at 45º with xaxis
(4) V/m at –45º with xaxis
25 Determine the electric field strength vector if the potential of this field depends on x, y coordinates as V = 10 axy –
(1) (2)
(3) (4)
26 An electric dipole of length 2 cm is placed with its axis making an angle of 30º to a uniform electric field 105 N/C. If it experiences a torque of Nm, then potential energy of the dipole
(1) –10 J (2) –20 J
(3) – 30 J (4) –40 J
7 Two isolated metallic solid spheres of radii R and 2R are charged, such that both of these have same charge density s. The spheres are located far away from each other and connected by a thin conducting wire. The new charge density on the bigger sphere is
(1) (2)
(3) (4) .
28 Electric potential in an electric field is given as V= K/r, (K being constant), if position vector then electric field will be
(1) (2) (3) (4)
29 At any point ( x,0,0) the electric potential V is volt, then electric field at x = 1 m –
(1) (2)
(3) (4)
30 8 small droplets of water of same size and same charge form a large spherical drop. The potential of the large drop, in comparision to potential of a small drop will be –
(1) 2 times (2) 4 times (3) 8times (4) same
31 As per this diagram a point charge +q is placed at the origin O. Work done in taking another pont charge –Q from the point A [coordinates (0, a)] to another point B [coordinates (a,0)] along the straight path AB is
(1) Zero (2)
(3) (4)
32 Determine dimensions of e0 (permitivity of free space) –
(1) [M–1L–3T4A2] (2) [M–1L–3T2A4] (3) [ML3T–4A–2] (4) [M–1L–3T2A2]
33 If in Millikan’s oil drop experiment charges on drops are found to be 8µC, 12µC, 20µC, then quanta of charge is
(1) 8µC (2) 4µC
(3) 20µC (4) 12µC
34 Force between two identical spheres charged with same charge is F. If 50% charge of one sphere is transffered to second sphere then new force will be
(1) (2)
(3) (4) none of these
35 In the electric field of charge Q, another charge is carried from A to B, A to C, A to D and A to E, then work done will be
(1) minimum along path AB (2) minimum along path AD
(3) minimum along path AE (4) zero along all the paths
6 The total flux associated with given cube will be where ‘a’ is side of cube –
(=4p × 9 ×109)
(1) 162p × 10–3 Nm2/C (2) 162p × 103 Nm2/C (3) 162p × 10–6 Nm2/C (4) 162p × 106 Nm2/C
37 A sphere of 4 cm radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is charged to a potential 3 e.s.u. When the outer sphere is earthed. The charge on the inner sphere is –
(1) 54 e.s.u. (2) e.s.u.
(3) 30 e.s.u. (4) 36 e.s.u.
38 Two identical small spheres carry charge of Q1 and Q2 with Q1 >> Q2. The charges are d distance apart. The force they exert on one another is F1. The spheres are made to touch one another and then separated to distance d apart. The force they exert on one another now is F2. Then F1/F2 is
(1) (2) (3) (4)
39 A point particle of mass M is attached to one end of a massless rigid nonconducting rod of length L. Another point particle of same mass is attached to the other end of the rod. The two particles carry charges +q and –q respectively. This arrangement is held in a region of uniform electric field E such that the rod makes a small angle q(<5º) with the field direction. The minimum time needed for the rod to become parallel to the field after it is set free.( rod rotates about centre of mass)
(1) (2)
(3) (4)
in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is , where k is
(1) 8q2 (2) 6q2 (3) 8q1 (4) 6q1
41 The electric potential at a point (x, y, z) is given by
V = –x2y – xz3 + 4
The electric field at that point is
(1) (2)
(3)
(4)
42 Three concentric spherical shells have radii a, b and c(a < b < c) and have surface charge densities s, –s and s respectively. If VA, VB and VC denote the potentials of the three shells, then, for
c = a + b, we have
(1) VC = VB = VA (2) VC = VA ¹ VB
(3) VC = VB ¹ VA (4) VC ¹ VB ¹ VA
43 The figure shows some of the electric field lines corresponding to an electric field.
The figure suggests –
(1) EA > EB > EC
(2) EA = EB = EC
(3) EA = EC > EB
(4) EA = EC < EB
4 Two identical thin rings, each of radius R meters, are coaxially placed at a distance R meters apart. If Q1 coulomb and Q2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is
(1) zero
(2)
(3)
(4)
45 Three charges –q1, +q2 and –q3 are placed as shown in the figure. The xcomponent of the force on –q1 is proportional to
(1) (2)
(3) (4)
Answer Key
Q.N. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Ans. 1 3 4 1 2 2 3 1 2 2 2 2 1 1 3 1 1 3 1 3 1 2 1 1
Q.N 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
ANS. 2 3 2 2 2 2 1 1 2 1 4 2 4 3 3 1 2 2 3 2 3
ELECTROSTATICS
exercise # 1
Question based on coulomb’s law
1 An electron at rest has a charge of 1.6 × 10–19 C. It starts moving with a velocity v = c/2, where c is the speed of light, then the new charge on it is –
(1) 1.6 × 10–19 Coulomb
(2) 1.6 × 10–19 Coulomb
(3) 1.6 × 10–19 Coulomb (4) Coulomb
2 Two similar charge of +Q , as shown in figure are placed at A and B. –q charge is placed at point C midway between A and B. –q charge will oscillate if
A c B
+Q——— q ———— +Q
(1) It is moved towards A. (2) It is moved towards B.
(3) It is moved upwards AB.
(4) Distance between A and B is reduced.
3 When the distance between two charged particle is halved, the force between them becomes –
(1) One fourth (2) One half (3) Double (4) Four times
4 Two charges are at distance (d) apart in air. Coulomb force between them is F. If a dielectric material of dielectric constant (K) is placed between them, the coulomb force now becomes.
(1) F/K (2) FK (3) F/K2 (4) K2F
5 A certain charge Q is divided at first into two parts, (q) and (Qq). Later on the charges are placed at a certain distance. If the force of interaction between the two charges is maximum then
(1) (Q/q) = (4/1) (2) (Q/q) = (2/1)
(3)(Q/q) = (3/1) (4) (Q/q) = (5/1)
6 The three charges each of 5 × 10–6 coloumb are placed at vertex of an equilateral triangle of side 10cm. The force exerted on the charge of 1 m C placed at centre of triangle in newton will be
(1) 13.5 (2) zero
(3) 4.5 (4) 6.75
7 ABC is a right angle triangle AB=3cm, BC=4cm charges + 15, +12, –12 esu are placed at A, B and C respectively. The magnitude of the force experienced by the charge at B in dyne is
(1) 125 (2) 35
(3) 22 (4) 0
8 Five point charges, each of value +q coulomb, are placed on five vertices of a regular hexagon of side L metre. The magnitude of the force on a point charge of value q coul. placed at the centre of the hexagon is –
(1) (2)
(3) (4) Zero
9 Two charged spheres A and B are charged with the charges of +10 and +20 coul. respectively and separated by a distance of 80cm. The electric field at a point on the line joining the centres of the two sphers will be zero at a distance from sphere A.
(1) 20 cm (2) 33 cm (3) 55 cm (4) 60 cm.
10 Four charges +q, +q, –q and –q are placed respectively at the corners A, B, C and D of a square of side (a), arranged in the given order. Calculate the intensity at (O) the centre of the square .
(1) (2) (3) (4)
11 The electric potential V at any point (x, y, z) in space is given by V = 4×2 volt. The electric field E in V/m at the point (1, 0, 2) is –
(1) +8 in x direction (2) 8 in –x direction (3) 16 in + x direction (4) 16 in –x direction
12 Charges of + × 10–9 are placed at each of the four corners of a square of side 8cm. The potential at the intersection of the diagonals is
(1) 150 Volt (2) 1500 Volt
(3) 900 Volt (4) 900 Volt
13 The electron potential (V) as a function of distance (x) [in meters] is given by
V = (5×2 + 10 x – 9)Volt.
The value of electric field at x =1m would be
(1) 20 Volt/m (2) 6 Volt/m (3) 11 Volt/m (4) –23 Volt/m
14 A – particle moves towards a rest nucleus, if kinetic energy of particle is 10 MeV and atomic number of nucleus is 50. The closest approach will be –
(1) 1.44 × 10–14 m (2) 2.88 × 10–14 m (3) 1.44 × 10–10 m (4) 2.88 × 10–10 m
15 A charge of Q coloumb is located at the centre of a cube. If the corner of the cube is taken as the origin, then the flux coming out from the faces of the cube in the direction of X axis will be
(1) 4 (2) Q/6 (3) Q/3 (4) Q/4
16 A rectangular surface of 2 metre width and 4 metre length, is placed in an electric field of intensity 20 newton/C, there is an angle of 60º between the perpendicular to surface and electrical field intensity. Then total flux emitted from the surface will be (In Volt metre)
(1) 80 (2) 40
(3) 20 (4) 160
17 A square of side 20cm. is enclosed by a surface of sphere of 80 cm. radius . square and sphere have the same centre. four charges +2 × 10–6 c, –5 × 10–6 c, –3 × 10–6 c, +6 × 10–6c are located at the four corners of a square, Then out going total flux from spherical surface in Nm2/c will be
(1) zero (2) (16p) × 10–6
(3) (8p) × 10–6 (4) (36 p) × 10–6
18 A charge Q is distributed over two concentric hollow spheres of radii (r) and (R) > (r) such the surface densities are equal. Find the potential at the common centre.
(1) (2)
(3) (4) none of these
19 A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of 3Q the new potential difference between the same two surfaces is
(1) V (2) 2V
(3) 4V (4) –2V
20 An electric dipole consists of two opposite charges each of magnitude 1 × 10–6 C separated by a distance 2cm. The dipole is placed in an external field of 10 × 105N/C. The maximum torque on the dipole is –
(1) 0.2 × 10–3 Nm
(2) 1.0 × 10–3 Nm
(3) 20 × 103 Nm
(4) 4 × 10–3 Nm
21 If an electric field is given by , calculate the electric flux through a surface of area 10 units lying in yz plane
(1) 100 units (2) 10 units
(3) 30 units (4) 40 units
22 Two long thin charged rods with charge density l each are placed parallel to each other at a distance d apart. The force per unit length exerted on one rod by the other will be
(1) (2)
(3) (4)
23 The electric field intensity due to a thin infinite long straight wire of uniform linear charge density l at O is –
(1) (2)
(3) (4) Zero
24 Figure shows a set of euipotential surfaces. The magnitude and direction of electric field that exists in the region is
(1) V/m at 45º with xaxis
(2) V/m at –45º with xaxis
(3) V/m at 45º with xaxis
(4) V/m at –45º with xaxis
25 Determine the electric field strength vector if the potential of this field depends on x, y coordinates as V = 10 axy –
(1) (2)
(3) (4)
26 An electric dipole of length 2 cm is placed with its axis making an angle of 30º to a uniform electric field 105 N/C. If it experiences a torque of Nm, then potential energy of the dipole
(1) –10 J (2) –20 J
(3) – 30 J (4) –40 J
7 Two isolated metallic solid spheres of radii R and 2R are charged, such that both of these have same charge density s. The spheres are located far away from each other and connected by a thin conducting wire. The new charge density on the bigger sphere is
(1) (2)
(3) (4) .
28 Electric potential in an electric field is given as V= K/r, (K being constant), if position vector then electric field will be
(1) (2) (3) (4)
29 At any point ( x,0,0) the electric potential V is volt, then electric field at x = 1 m –
(1) (2)
(3) (4)
30 8 small droplets of water of same size and same charge form a large spherical drop. The potential of the large drop, in comparision to potential of a small drop will be –
(1) 2 times (2) 4 times (3) 8times (4) same
31 As per this diagram a point charge +q is placed at the origin O. Work done in taking another pont charge –Q from the point A [coordinates (0, a)] to another point B [coordinates (a,0)] along the straight path AB is
(1) Zero (2)
(3) (4)
32 Determine dimensions of e0 (permitivity of free space) –
(1) [M–1L–3T4A2] (2) [M–1L–3T2A4] (3) [ML3T–4A–2] (4) [M–1L–3T2A2]
33 If in Millikan’s oil drop experiment charges on drops are found to be 8µC, 12µC, 20µC, then quanta of charge is
(1) 8µC (2) 4µC
(3) 20µC (4) 12µC
34 Force between two identical spheres charged with same charge is F. If 50% charge of one sphere is transffered to second sphere then new force will be
(1) (2)
(3) (4) none of these
35 In the electric field of charge Q, another charge is carried from A to B, A to C, A to D and A to E, then work done will be
(1) minimum along path AB (2) minimum along path AD
(3) minimum along path AE (4) zero along all the paths
6 The total flux associated with given cube will be where ‘a’ is side of cube –
(=4p × 9 ×109)
(1) 162p × 10–3 Nm2/C (2) 162p × 103 Nm2/C (3) 162p × 10–6 Nm2/C (4) 162p × 106 Nm2/C
37 A sphere of 4 cm radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is charged to a potential 3 e.s.u. When the outer sphere is earthed. The charge on the inner sphere is –
(1) 54 e.s.u. (2) e.s.u.
(3) 30 e.s.u. (4) 36 e.s.u.
38 Two identical small spheres carry charge of Q1 and Q2 with Q1 >> Q2. The charges are d distance apart. The force they exert on one another is F1. The spheres are made to touch one another and then separated to distance d apart. The force they exert on one another now is F2. Then F1/F2 is
(1) (2) (3) (4)
39 A point particle of mass M is attached to one end of a massless rigid nonconducting rod of length L. Another point particle of same mass is attached to the other end of the rod. The two particles carry charges +q and –q respectively. This arrangement is held in a region of uniform electric field E such that the rod makes a small angle q(<5º) with the field direction. The minimum time needed for the rod to become parallel to the field after it is set free.( rod rotates about centre of mass)
(1) (2)
(3) (4)
in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is , where k is
(1) 8q2 (2) 6q2 (3) 8q1 (4) 6q1
41 The electric potential at a point (x, y, z) is given by
V = –x2y – xz3 + 4
The electric field at that point is
(1) (2)
(3)
(4)
42 Three concentric spherical shells have radii a, b and c(a < b < c) and have surface charge densities s, –s and s respectively. If VA, VB and VC denote the potentials of the three shells, then, for
c = a + b, we have
(1) VC = VB = VA (2) VC = VA ¹ VB
(3) VC = VB ¹ VA (4) VC ¹ VB ¹ VA
43 The figure shows some of the electric field lines corresponding to an electric field.
The figure suggests –
(1) EA > EB > EC
(2) EA = EB = EC
(3) EA = EC > EB
(4) EA = EC < EB
4 Two identical thin rings, each of radius R meters, are coaxially placed at a distance R meters apart. If Q1 coulomb and Q2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is
(1) zero
(2)
(3)
(4)
45 Three charges –q1, +q2 and –q3 are placed as shown in the figure. The xcomponent of the force on –q1 is proportional to
(1) (2)
(3) (4)
Answer Key
Q.N. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Ans. 1 3 4 1 2 2 3 1 2 2 2 2 1 1 3 1 1 3 1 3 1 2 1 1
Q.N 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
ANS. 2 3 2 2 2 2 1 1 2 1 4 2 4 3 3 1 2 2 3 2 3
]]>A system of closely spaced charges is said to form a continuous charge distribution. It is useful to consider the density of a charge distribution as we do for density of solid, liquid, gas, etc.
(i) Line or Linear Charge Density ( λ): If the charge is distributed over a straight line or over the circumference of a circle or over the edge of a cuboid, etc, then the distribution is called “linear charge distribution”. Linear charge density is the charge per unit length. Its SI unit is C / m.
(ii) Surface Charge Density ( σ) : σ= qSσ= dqdSorIf the charge is distributed over a surface area, then the distribution is called ‘surface charge distribution’.Surface charge density is the charge per unit area. Its SI unit is C / m2.
Total charge on surface S, q = ∫σdSS
(iii) Volume Charge Density ( ρ):ρ= qזρ= dqd זorIf the charge is distributed over a volume, then the distribution is called ‘volume charge distribution’. Volume charge density is the charge per unit volume. Its SI unit is C / m3
]]>Glass + Silk—– Glass(+) + Silk()
Ebonite rod + Cat far—– Ebonite rod() + Cat far(+)
in glass are loosely bound in it than the electrons in silk. So, when glass and silk are rubbed together, the comparatively loosely bound electrons from glass get transferred to silk. As a result, glass becomes positively charged and silk becomes negatively charged. Electrons in fur are loosely bound in it than the electrons in ebonite. So, when ebonite and fur are rubbed together, the comparatively loosely bound electrons from fur get transferred to ebonite. As a result, ebonite becomes negatively charged and fur becomes positively.
2. Conduction
The process of transfer of charge by contact of two bodies is known as conduction. If a charged body is put in contact with uncharged body, the uncharged body becomes charged due to transfer of electrons from one body to the other.
3. Electrostatic induction
If a charged body is brought near a neutral body, the charged body will attract opposite charge and repel similar charge present in the neutral body. As a result of this one side of the neutral body becomes negative while the other positive, this process is called ‘electrostatic induction’.
]]>6. Charge is quantised. the minimum value of charge is fixed that is know as quanta, it represented by e.
The quantization of electric charge is the property by virtue of which all free charges are integral multiple of “e” . Thus charge q of a body is always given by e .
q = ne n = positive integer or negative integer
The quantum of charge is the charge that an electron or proton carries.
Note : Charge on a proton = – charge on an electron = 1.6 × 10–19 C
In an isolated system, total charge does not change with time, though individual charge may change, charge can neither be created nor destroyed. Conservation of charge is also found to hold good in all types of reactions either chemical(atomic) or nuclear. No exceptions to the rule have ever been found.
7. Charge is invariant . Charge is independent of frame of reference, charge on a body does not change what ever be its speed.
8. Similar charges repel each other while dissimilar attract
]]>charge is the fundamental physical property matter, it create different phenomena from initial. A scale can’t attract dust particle without rubbing by hair, in initial condition scale not attract dust particle.
History of charge
In 600 BC first of all “Thales” use charge word in his experiment, Thales of Miletus, one of the founders of Greek science, first noticed that if a piece of amber is rubbed with a woolen cloth, it then acquires the property of attracting light feathers, dust, lint, pieces of leaves, etc.
After this
In 1600 A.D. William Gilbert, the personal doctor to Queen Elizabeth – I of England, made a systematic study of the substances that behave like amber. In his book De Magnete (on the magnet), he introduced static electricity using amber; amber is called electron in Greek, so Gilbert decided to call its effect the electric force. He invented the first electrical measuring instrument, the electroscope, in the form of a pivoted needle he called the versorium.
Benjamin Franklin (17061790), an American pioneer of electrostatics introduced the presentday convention by replacing with silk bu the terms vitreous and resinous by positive and with flanne negative, respectively. According to this convention :
gives a list of the pairs of objects which get matter, the po charged on rubbing against each other. On rubbing, an object of column I will acquire positive charge while bulk is electric that of column II will acquire negative charge.
electron charge
The electro loosely bound remove an ele called its work are rubbed agai from the mate material with glass rod devel negative charg combined total still zero, as it w conserved duri
when a glass electrons are tr
of electrons w
Electric orig
which an electr to exert a stror actually transfe rubbing, so fricti
Table : Two kinds of charges developed on rubbing
(Positive charge)  (Negative charge) 
Glass rod  Silk cloth 
Woollen carpet  Rubber shoes 
Flannel or cat skin  Ebonite rod 
Woollen cloth  Amber rod 
Woollen coat  Plastic seat 
Obviously, any two charged objects belonging to the same column will repel each other while those of two different columns will attract each other.
NOTE : Benjamine’s choice of positive and negative charges is purely conventional one.
Unit of charge
S.I / M.K.S. unit of charge is Coulomb “C”
C.G.S unit of charge is e.s.u ( electro state unit ) or su
smallest unit of charge is franklin “fr”
1 esu/su = 3*10^{9 }C
Charge in motion than its unit emu (electro magnetic unit )
1 emu of charge =10C
Biggest unit of charge is faraday “F”
1 F = 96500C / 1 F = 96550C
]]>1. क्रमबद्ध त्रुटि: किसी भौतिक राषि के मापन मे वे त्रुटिया जिनके बीच का अन्तराल निष्चित होता है। अथवा जव किसी त्रुटि का मान एक निष्चित अन्तराल के बाद
पुनरावृति हो तो क्रमबद्ध त्रुटिया कहते है। यह पाॅच प्रकार की होती है।
1(A) व्यक्तिगत त्रुटि: वे त्रुटिया जो व्यक्ति की कमी के कारण उत्पन्न होती है। अथवा किसी प्रयोग के दोरान व्यक्ति जो त्रुटिया करता है। उसे व्यक्तिगत त्रुटि कहते है।
इसे दूर करने के लिए हमे सम्पूर्ण सावधानी रखनी चाहिए ।
1(B) पूर्णयास्थ त्रुटि: वे त्रुटिया जो किसी प्रयोग के दौरान निष्चित रूप से उत्पन्न होती है। पूर्णयास्थ त्रुटि कहते है।
इसे दूर करने के लिए हमे सामान्य ताप दाब एंव पदार्थ की भौतिक अवस्थाओ को ध्यान मे रखकर प्रयोग करने चाहिए।
1(C) यात्रिंक त्रुटि: वे त्रुटि जो किसी प्रयोग के दौरान यंत्र की अपूर्णता के कारण उत्पन्न होती है। यात्रिंक त्रुटि कहलाती है। इस प्रकार की त्रुटि को दूर करने के लिए सही
उपकरणो का प्रयोग करना चाहिए ।
1(D) निश्चित त्रुटि: वे त्रुटिया जो किसी प्रयोग के दौरान नियमित अन्तराल के बाद उत्पन्न होती है। निष्चित त्रुटि कहलाती है।
1(E) अनिष्चित त्रुटि: वे त्रुटिया जो किसी प्रयोग के दौरन अनिष्चित अंतराल के बाद उत्पन्न होती है अनिष्चित त्रुटि कहलाती है।
2. यादृच्छिक त्रुटि: इस प्रकार की त्रुटि का प्रयोग के दौरान आकस्मिक अचानक तथा यादृच्छिक रूप से उत्पन्न होती हैं । ये त्रुटिया यादृच्छिक त्रुटिया कहलाती है।
माना किसी भौतिक राषि के मापन मे q_{1}, q_{2, }q_{3, }q_{4, }q_{5 } प्रेक्षण लिए जाते है। तो इन प्रेक्षण का माध्य मान A_{m } ही भौतिक राषि का वास्तविक मान कहलाता है।
माध्यमान = q_{1}+q_{2}+q_{3}+q_{4}+q_{5} / 5
3 स्थूल त्रुटिया: वे त्रुटिया जो प्रयोग के दौरान स्थूलता के कारण उत्पन्न होती है। स्थूल त्रुटिया कहलाती है। ये निम्न कारणो से होती है।
भौतिक राषि:प्रकृति मे जो कुछ हमे दिखाता है। जिसे हम छू सकते है। जिसे हम महसूस कर सकते है। अथवा वे राषियाॅ वस्तुए जिन्है मापा या तौला जा सकता है भौतिक
राशिया कहलाती है। ये दो प्रकार की होती है।
मूल भौतिक राषि: वे राषिया जिन्है व्यक्त करने के लिए किसी अन्य भौतिक राषि की आवष्यकता नही होती है मूल राषिया कहलाती है।
क्रम संख्या  राशि  मात्रक  प्रतीक 
1.  द्रव्यमान  किलाग्राम  kg 
2.  लम्बाई  मीटर  M 
3.  समय  सैकेण्ड  S/sec 
4.  विद्युत धारा  एम्पीयर  A 
5.  ताप  केल्विन  K 
6.  पदार्थ की मात्रा  मोल  Mol 
7.  ज्योति तीव्रता  केण्डेला  Cd 
पूरक मात्रक: वे भौतिक मात्रक जिन्है व्यक्त करने के लिए किसी अन्य भौतिक राषि की आवष्यकता नही होती एंव मूल मात्रको के समतुल्य हो। पूरक मात्रक कहलाते है।
1. कोण= कोण एक मात्रक हीन राषि है फिर भी इसे डिग्री रेडियन मिनट सैकेण्ड मे मापा जाता है। 2. घन कोण=

वे भातिक राष्यिाॅ जिन्है व्यक्त करने के लिए मूल भौतिक राषि की आवष्यकता होती है। व्युत्पन्न राषियाॅ कहलाती है।
वेग, चाल, तवरण, कार्य, शक्ति, संवेग, बलाघूर्ण, आदि 
लम्बाई का मापन: 10^{3 }मी से 10^{1} मी तक की लम्बाई का मापन निम्न के द्वारा की जाती है
1.स्फेरोमीटर
2. वर्नियर कैलिपर्स
3. स्क्रू गेज
1 मी से 10^{4 }मी तक की लम्बाई का मापन निम्न के द्वारा की जाती है
स्केल
फीता
इंचटेप
वृहत दूरियो का मापन:–
खगोलीय मात्रक: पृथ्वी के केन्द्र से सूर्य के केन्द्र की बीच की दूरी खगोलीय मात्रक कहलाती है
1 AU=1.496*10^{11 }मी
1 AU= 1.5*10^{11 }मी
प्रकाश वर्ष: निर्वात मे सूर्य की तरग द्वारा एक वर्ष मे चली गई दूरी प्रकाष वर्ष कहलाता है।
1 प्रकाश वर्ष = 3*10^{8} * 365*24*60*60= 9.1*10^{15} मी
पारसेक: यह लम्बाई दूरी का सबसे बडा मात्रक है। यह सूर्य के चारो और चक्कर लगाते समय पृथ्वी द्वारा एक आर्क कोण मे चली गई दूरी होती है।
1 पारसेक = 3*10^{16 } मी
लंबन विधि: वृहत दूरीयो को ज्ञात करने के लिए लंबन विधि का उपयोग किया जाता है इस विधि के अन्र्तगत हम एक पेन्सिल को अपनी आखे के सामने रखकर बाॅयी आखे को बन्द करके दायी आखे से उस वस्तु को देखते है। इसके बाद मे फिर दायी आखे को बन्द करके वायी आखे से उस वस्तु को देखते है । तो हम पाते है कि वस्तु की स्थिति मे कोण का परिवर्तन होता है इस परिवर्तन कोण को लंबन कोण कहते है। तथा इस विधि को लंबन विधि इ कहते है।
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