# which of the following options is correct? in a region of constant potential

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## In a region of constant potential:

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Question

## In a region of constant potential:

**A**

## the electric field is uniform.

**B**

## the electric field is zero.

**C**

## there can be no charge inside the region.

**D**

## both (b) and (c) are correct.

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is D)

In a region of constant potentialE=− dr dV =0 (∵ V= constant)

i.e., electric field is zero, so there can be no charge inside the region.

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## In a region of constant potential

In a region of constant potential E=-"dV"/"dr"=0 " " (because "V=constant") i.e., electric field is zero , so there can be no charge inside the region.

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In a region of constant potent...

In a region of constant potential

Updated On: 27-06-2022

( 00 : 010 ) ADVERTISEMENT Text Solution Open Answer in App A

the electric field is uniform.

B

the electric field is zero.

C

there can be no charge inside the region.

D

both (b) and (c ) are correct.

Answer

The correct Answer is D

Solution

In a region of constant potential

`E=-"dV"/"dr"=0 " " (because "V=constant")`

i.e., electric field is zero , so there can be no charge inside the region.

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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## In a region of constant potential:A. The electric field is uniform.B. The electric field is zero.C. There can be no charge inside the region.D. Both (B) and (C) are correct.

In a region of constant potential:A. The electric field is uniform.B. The electric field is zero.C. There can be no charge inside the region.D. Both (B) and (C) are correct.. Ans: Hint: The electric field is the negative differentiation of potential ...

In a region of constant potential:A. The electric field is uniform.

B. The electric field is zero.

C. There can be no charge inside the region.

D. Both (B) and (C) are correct.

Answer Verified 231.9k+ views 2 likes

**Hint:**The electric field is the negative differentiation of potential with respect to the small displacement dx. We know that charge produces electric fields. If there is an electric field in that region, there should be charges present in the region.

**Complete answer:**

To answer this question, we use the relation between electric potential and electric field.

The electric field in the region of potential difference is expressed as,

E=− dV dx E=−dVdx ……. (1) Here, dV dV

is the potential difference and

dx dx

is the small displacement.

We have given that the potential is constant in the given region. Therefore,

V=constant V=constant

The electric field will be uniform in the given region if and only if there is linear change in potential with the distance x. Since the potential does not change. The electric field cannot be uniform. Therefore, the option (A) is incorrect.

Since V is constant, the electric field,

E=− dV dx =0 E=−dVdx=0

Therefore, the electric field in this region is zero. We know that charge produces electric fields. Since there is no electric field in the given region, we can say there are no any charges in the region.

**So, the correct answer is option (B) and (C).**

**Note:**Equation (1) is obtained from expression of work done to move the point charge in the potential difference. The work done to move the unit charge is equal to potential difference between two points. The negative sign in the above equation denotes that we are moving the charge against the electric force acting on it.

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Related Questions Question 1

Which of the following is true for the uniform electric field?

A) All the points are at the same potential.

B) No two points can have the same potential.

C) Pairs of points separated by the different distance must have the same difference in potential.

D) None of these Question 2

The potential at a point

(x,0,0) (x,0,0) is given by V=( 1000 x + 1500 x 2 + 500 x 3 )

V=(1000x+1500x2+500x3)

. Find the field intensity at the point where

x=1m x=1m (A) E x =5500 i ˆ V m −1 Ex=5500i^Vm−1 (B) E x =55 i ˆ V m −1 Ex=55i^Vm−1 (C) E x =550 i ˆ V m −1 Ex=550i^Vm−1 (D) E x =5.5 i ˆ V m −1 Ex=5.5i^Vm−1 Question 3

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density

λ λ

are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is (are)

A) both charges execute simple harmonic motion

B) both charges continue to move in the direction of their displacement

C) charge +q executes simple harmonic motion while -q continues moving in direction of its displacement

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