A charge of 8 mC is located at the origin. Calculate the work done by external agent in taking a small charge of – 2 × 10 – 9 C from a point A ( 0 , 0 , 0 . 03 m ) to a point B ( 0 , 0 . 04 m , 0 ) via a point C ( 0 , 0 . 06 m , 0 . 09 m ) .

Given, Charge located at the origin, q = 8 mC = 8 × 10 - 3 C . The small charge that it taken around, q 1 = - 2 × 10 - 9 C . Distance of a point P from the origin, d 1 = 3 × 10 - 2 m . Distance of a point Q from the origin, d 2 = 4 × 10 - 2 m . The potential energy of q 1 when it is at a point P is, V P = q q 1 4 π ε 0 d 1 = 9 × 10 9 × ( 8 × 10 - 3 ) × ( - 2 × 10 - 9 ) 3 × 10 - 2 = - 4 . 8 J The potential energy of q 1 when it is at a point Q is, V Q = q q 1 4 π ε 0 d 2 = 9 × 10 9 × ( 8 × 10 - 3 ) × ( - 2 × 10 - 9 ) 4 × 10 - 2 = - 3 . 6 J The electric field is a conservative field. Hence, the work done on the charge is nothing but the change in the potential energy irrespective of the path. Therefore, the work done, W = V Q - V P = - 3 . 6 - ( - 4 . 8 ) = 1 . 2 J .

A charge of 8 mC is located at the origin. Calculate the work done by external agent in taking a small charge of – 2 × 10 – 9 C from a point A ( 0 , 0 , 0 . 03 m ) to a point B ( 0 , 0 . 04 m , 0 ) via a point C ( 0 , 0 . 06 m , 0 . 09 m ) .

Given, Charge located at the origin, q = 8 mC = 8 × 10 - 3 C . The small charge that it taken around, q 1 = - 2 × 10 - 9 C . Distance of a point P from the origin, d 1 = 3 × 10 - 2 m . Distance of a point Q from the origin, d 2 = 4 × 10 - 2 m . The potential energy of q 1 when it is at a point P is, V P = q q 1 4 π ε 0 d 1 = 9 × 10 9 × ( 8 × 10 - 3 ) × ( - 2 × 10 - 9 ) 3 × 10 - 2 = - 4 . 8 J The potential energy of q 1 when it is at a point Q is, V Q = q q 1 4 π ε 0 d 2 = 9 × 10 9 × ( 8 × 10 - 3 ) × ( - 2 × 10 - 9 ) 4 × 10 - 2 = - 3 . 6 J The electric field is a conservative field. Hence, the work done on the charge is nothing but the change in the potential energy irrespective of the path. Therefore, the work done, W = V Q - V P = - 3 . 6 - ( - 4 . 8 ) = 1 . 2 J .

In front of a uniformly charged infinite non-conducting sheet of surface charge density σ , a point charge q 0 is shifted slowly from a distance a to b b > a . If work done by an external agent is W , then find out the relation between the given parameters.

Electric field due to the uniformly charged infinite sheet E = σ 2 ε 0 The electric field is constant, and it will exert a constant force on the charge F = q 0 E . Therefore, an external agent has to apply the same force in opposite direction to shift it slowly Work done by a constant force W = F → · d → W = q 0 E b - a ⇒ W = q 0 σ 2 ε 0 b - a ⇒ W = σ q 0 b - a 2 ε 0 .

A particle of charge + 3 × 10 - 9 C is in a uniform field directed to the left. It is released from rest and moves a distance of 5 cm , after which its kinetic energy is found to be 4 . 5 × 10 - 5 J . a What work was done by the electrical force? b What is the magnitude of the electrical field? c What is the potential of the starting point with respect to the endpoint?

When a charge is released in an electric field, the electric field exerts a force on it, and it gets accelerated. Its speed increases and it gains kinetic energy. In other words, we may say work done by the electric field on charge changes its kinetic energy. a Work done by electric force W = ∆ K E = 4 . 5 × 10 - 5 - 0 W = 4 . 5 × 10 - 5 J . b F × d = ∆ K E Q E × d = ∆ K E 3 × 10 - 9 × E × 0 . 05 = 4 . 5 × 10 - 5 E = 3 × 10 5 N C - 1 . c E = - d V d r - ∫ 1 2 d V = E ∫ 0 0 . 05 d r ⇒ V 1 - V 2 = - 3 × 10 5 × 0 . 05 - 0 ⇒ ∆ V 12 = 1 . 5 × 10 4 V .

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

A charge of $8 mC$ is located at the origin. Calculate the work done by external agent in taking a small charge of $- 2 \times 10^{- 9} C$ from a point $A (0, 0, 0.03 m)$ to a point $B (0, 0.04 m, 0)$ via a point $C (0, 0.06 m, 0.09 m) .$

Important Questions on Electrostatics

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 28

A positive charge $Q = 50 μC$ is located in the $x y$ plane at a point having position vector $\overset{⇀}{r_{0}} = (2 \overset{⏜}{i} + 3 \hat{j}) m$ , where $\hat{i}$ and $\hat{j}$ are unit vectors in the positive directions of $X$ and $Y$ axis, respectively. Find:

$(a)$ The electric intensity vector and its magnitude at a point having coordinates $(8 m, - 5 m)$ .

(b)

Work done by an external agent in transporting a charge

q = 10 μC

from

(8 m, 6 m)

to the point

(4 m, 3 m)

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 29

Four charges $+ q$ , $+ q$ , $- q$ and $- q$ are fixed respectively at the corners of $A$ , $B$ , $C$ and $D$ of a square of side $a$ arranged in the given order. Calculate the electric potential and intensity at $O$ (Centre of the square). If $E$ and $F$ are the midpoints of sides $B C$ , $C D$ , respectively, what will be the work done by an external agent in carrying a charge $Q$ slowly from $O$ to $E$ and from $O$ to $F$ ?

Question Image

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 30

A charge

Q

is distributed over two concentric hollow spheres of radius

r

and

R (R > r)

, such that the surface densities of charge are equal. Find the potential at the common centre.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 31

Two uniformly charged concentric hollow spheres of radii

R

and

2 R

are charged. The inner sphere has a charge of

1 μC

and the outer sphere has a charge of

2 μC

of the same sign. The potential is

9000 V

at a point

P

at a distance

3 R

from the common centre

O

. What is the value of

R

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 32

In front of a uniformly charged infinite non-conducting sheet of surface charge density

σ

, a point charge

q_{0}

is shifted slowly from a distance

a

b (b > a)

. If work done by an external agent is

W

, then find out the relation between the given parameters.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 33

An electric field of $20 N C^{- 1}$ exists along the negative x-axis in space. Calculate the potential difference $V_{B} - V_{A}$ , where the points $A$ and $B$ are given by,

$(a)$ $A = (0, 0)$ , $B = (0, 4 m)$

$(b)$ $A = (2 m, 1 m)$ , $B = (4 m, 3 m)$

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 34

A uniform field of $8 N C^{- 1}$ exists in space in a positive $x$ -direction.

$(a)$ Taking the potential at the origin to be zero, write an expression for the potential at a general point $(x, y, z)$ .

$(b)$ At which points, the potential is $160 V$ ?

$(c)$ If the potential at the origin is taken to be $80 V$ , what will be the expression for the potential at a general point?

$(d)$ What will be the potential at the origin if the potential at $x =$ infinity is taken to be zero?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 1>Q 35

A particle of charge $+ 3 \times 10^{- 9} C$ is in a uniform field directed to the left. It is released from rest and moves a distance of $5 cm$ , after which its kinetic energy is found to be $4.5 \times 10^{- 5} J$ .

$(a)$ What work was done by the electrical force?

$(b)$ What is the magnitude of the electrical field?

$(c)$ What is the potential of the starting point with respect to the endpoint?

A charge of 8 mC is located at the origin. Calculate the work done by external agent in taking a small charge of –2 × 10–9 C from a point A(0, 0, 0.03 m) to a point B(0, 0.04 m, 0) via a point C( 0, 0.06 m, 0.09 m).

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

A charge of $8 mC$ is located at the origin. Calculate the work done by external agent in taking a small charge of $- 2 \times 10^{- 9} C$ from a point $A (0, 0, 0.03 m)$ to a point $B (0, 0.04 m, 0)$ via a point $C (0, 0.06 m, 0.09 m) .$