# Electric Field and Potential : JEE Level Objective Questions (Set 01)

This page contains an updated set of objective problems on the chapter '

*Electric Field and Potential*'.

**All the questions provided below strictly follow the current syllabus of JEE Mains & Advanced.**The carefully selected problems are arranged in a proper order according to the correct flow of topics in the syllabus.

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__Single Option Correct Type Questions__

__Single Option Correct Type Questions__

Out of the four different choices following each question, only one is the correct (or the most correct) which you have to mark.

2. Two point charges +9e and +e are placed 16 cm apart from each other. Where should a third charge q be positioned between them so that the system is in electrostatic equilibrium state?

4. Five positive equal charges are kept at vertices of a regular hexagon and resultant electric field at the centre is E. A negative charge having equal magnitude is kept at the sixth vertex and then the net electric field is E'. What is the value of E'/E?

5. A non-conducting ring of radius R contains uniformly distributed charge +Q. A tiny part of the ring, of length d, is removed (d << R). The net electric field at the centre of the ring will now be

6. Two equal negative charges -q are kept fixed at points (0, -a) and (0, a) on y-axis. A positive charge +Q is then released from rest at the point (2a, 0) on the x-axis. The point charge +Q will:

7. Two infinite linear charges are kept parallel to each other at a separation 0.1 m from each other. If the linear charge density on each is equal to 5 μC/m, then force acting on a unit length of each linear charge is

8. A point charge +50 μC is fixed in the xy plane at the point of position vector

10. A particle of mass m and charge q is kept in a sinusoidally varying electric field E' = Esinωt. It will undergo a simple harmonic motion of amplitude

12. Six point charges are arranged at the corners of a regular hexagon as shown in the below given figure.

13. A charged particle having some mass rests in equilibrium at a height h above the centre of a uniformly charged nonconducting horizontal ring of radius R. The force of gravity acts vertically downwards. The equilibrium of the particle will be stable :

14. An electron of mass m₁, initially at rest, covers a certain distance in a uniform electric field in time t₁. A proton of mass m₂, also, takes time t₂ to move through an equal distance (starting from rest) in this uniform electric field. Neglecting the effect of gravity, the ratio t₂/t₁ nearly equals

15. An alpha particle having energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of closest approach will be of the order

16. Two point charges q₁ and q₂ are located 3 m apart, and their sum of charges is 10 μC. If force of attraction between them is found to be 0.075 N then the values of q₁ and q₂ respectively, are :

17. Two positive and identical point charges are fixed at a certain distance. A third small charge is placed in between the two charges and it experiences zero resultant force due to the rest two.

18. Two particles of masses in the ratio 1 : 2 and with charges in the ratio 1 : 1 are placed at rest in a uniform electrostatic field. They are set free and allowed to move for the same time. The ratio of their kinetic energies would be finally

20. A point charge q is moved along a circle of radius r in the electric field of another point charge q' at the centre of the circular path. The work done by the electric field on the charge q in a half revolution will be

1. Taking mass (M), length (L), time (T) and current (I) as fundamental quantities, the dimensional formula of permittivity is :

- A) ML⁻²T²I

B) M⁻¹L⁻³T⁴I²

C) MLT⁻²I

D) ML²T⁻¹I²

**View Solution**

2. Two point charges +9e and +e are placed 16 cm apart from each other. Where should a third charge q be positioned between them so that the system is in electrostatic equilibrium state?

- A) 24 cm from +9e

B) 12 cm from +9e

C) 24 cm from +e

D) 12 cm from +e

- A) an increase in size

B) sometimes an increase and sometimes a decrease

C) no change in size

D) none of these

**View Solution**

4. Five positive equal charges are kept at vertices of a regular hexagon and resultant electric field at the centre is E. A negative charge having equal magnitude is kept at the sixth vertex and then the net electric field is E'. What is the value of E'/E?

- A) 2

B) 1

C) 3

D) None of these

**View Solution**

5. A non-conducting ring of radius R contains uniformly distributed charge +Q. A tiny part of the ring, of length d, is removed (d << R). The net electric field at the centre of the ring will now be

- A) directed towards the gap, inversely proportional to R³

B) directed towards the gap, inversely proportional to R²

C) directed away from the gap, inversely proportional to R³

D) directed away from the gap, inversely proportional to R²

**View Solution**

6. Two equal negative charges -q are kept fixed at points (0, -a) and (0, a) on y-axis. A positive charge +Q is then released from rest at the point (2a, 0) on the x-axis. The point charge +Q will:

- A) execute simple harmonic motion about origin

B) move to the origin and remain at rest

C) move to infinity

D) execute oscillatory but not simple harmonic motion

**View Solution**

7. Two infinite linear charges are kept parallel to each other at a separation 0.1 m from each other. If the linear charge density on each is equal to 5 μC/m, then force acting on a unit length of each linear charge is

- A) 2.5 N/m

B) 3.25 N/m

C) 4.5 N/m

D) 7.5 N/m

**View Solution**

8. A point charge +50 μC is fixed in the xy plane at the point of position vector

**rᤱ**= (2

**i**+ 3

**j**). What is the intensity of electric field at the point of position vector

**r**= (8

**i**- 5

**j**) m?

- A) 1200 V/m

B) 0.04 V/m

C) 900 V/m

D) 4500 V/m

9. Four point charges are arranged at the corners of a square ABCD, as shown in the figure.

The force experienced by a positive charge located at the centre of the square is :

- A) zero

B) along diagonal AC

C) along diagonal BD

D) perpendicular to the side AB

10. A particle of mass m and charge q is kept in a sinusoidally varying electric field E' = Esinωt. It will undergo a simple harmonic motion of amplitude

- A) qE²/mω²

B) qE/mω²

C) (qE/mω²)⁰·⁵

D) qE/mω

11. A charged particle of mass m and charge q is released from rest in a uniform electric field E. Neglecting the effect of gravity the kinetic energy attained by the particle after time 't' seconds is :

- A) Eqm/t

B) E²q²t²/2m

C) 2E²t²/mq

D) Eq²m/2t²

**View Solution**

12. Six point charges are arranged at the corners of a regular hexagon as shown in the below given figure.

If an electron is placed at the centre of the hexagon (point O), force on it will be

- A) zero

B) along OF

C) along OC

D) None of these

**View Solution**

13. A charged particle having some mass rests in equilibrium at a height h above the centre of a uniformly charged nonconducting horizontal ring of radius R. The force of gravity acts vertically downwards. The equilibrium of the particle will be stable :

- A) for all values of h

B) only if h > R/√2

C) only if h < R/√2

D) only if h = R/√2

**View Solution**

14. An electron of mass m₁, initially at rest, covers a certain distance in a uniform electric field in time t₁. A proton of mass m₂, also, takes time t₂ to move through an equal distance (starting from rest) in this uniform electric field. Neglecting the effect of gravity, the ratio t₂/t₁ nearly equals

- A) 1

B) (m₂/m₁)⁰·⁵

C) (m₁/m₂)⁰·⁵

D) 1836

**View Solution**

15. An alpha particle having energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of closest approach will be of the order

- A) 1 Angstrom

B) 10⁻¹⁰ cm

C) 10⁻¹² cm

D) 10⁻¹⁵ cm

**View Solution**

16. Two point charges q₁ and q₂ are located 3 m apart, and their sum of charges is 10 μC. If force of attraction between them is found to be 0.075 N then the values of q₁ and q₂ respectively, are :

- A) 5 μC, 5 μC

B) 15 μC, -5 μC

C) 5 μC, 15 μC

D) -15 μC, 5 μC

**View Solution**

17. Two positive and identical point charges are fixed at a certain distance. A third small charge is placed in between the two charges and it experiences zero resultant force due to the rest two.

- A) The equilibrium is stable if the small charge is positive

B) The equilibrium is stable if the small charge is negative

C) The equilibrium is always stable

D) The equilibrium is not stable

18. Two particles of masses in the ratio 1 : 2 and with charges in the ratio 1 : 1 are placed at rest in a uniform electrostatic field. They are set free and allowed to move for the same time. The ratio of their kinetic energies would be finally

- A) 2 : 1

B) 8 : 1

C) 4 : 1

D) 1 : 4

19. Three identical point charges each +q are fixed at the vertices of an equilateral triangle of side a. The Coulomb forced experienced by one of the charges due to the rest two is

- A) kq²/a²

B) 2kq²/a²

C) √3kq²/a²

D) zero

20. A point charge q is moved along a circle of radius r in the electric field of another point charge q' at the centre of the circular path. The work done by the electric field on the charge q in a half revolution will be

- A) zero

B) positive

C) negative

D) none of these

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