**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 (Q-q). 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 N-m2/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 N-m

(2) 1.0 × 10–3 N-m

(3) 20 × 10-3 N-m

(4) 4 × 10–3 N-m

**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 x-axis

(2) V/m at –45º with x-axis

(3) V/m at 45º with x-axis

(4) V/m at –45º with x-axis

**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 [co-ordinates (0, a)] to another point B [co-ordinates (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 non-conducting 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 x-component 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 (Q-q). 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 N-m2/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 N-m

(2) 1.0 × 10–3 N-m

(3) 20 × 10-3 N-m

(4) 4 × 10–3 N-m

**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 x-axis

(2) V/m at –45º with x-axis

(3) V/m at 45º with x-axis

(4) V/m at –45º with x-axis

**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 [co-ordinates (0, a)] to another point B [co-ordinates (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 non-conducting 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 x-component 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**