Question

What is the potential difference between two points, if 2J of work must be done to move a 4 mC charge from one point to another is:
A. 50 V
B. 500 V
C.5 V
D. 5000 V

Answer 1

To solve this problem, use the formula for work done to move a charge from one point to another in terms of potential difference and charge on the particle. Substitute the given values in the formula and solve it to find the potential difference between two points, if 2J of work must be done to move a 4 mC charge from one point to another.

Formula used:
$W= V \times Q$

Complete step-by-step solution:
Given:
Work done. W= 2J
Charge, $C= 4 mC= 4 \times {10}^{-3} C$

The formula for work done to move a charge from one point to another is given by,
$W= V \times Q$ …(1)
Where,
W is the work done to move a charge
V is the potential difference
Q is the charge of the particle

Substituting values in the equation. (1) we get,
$2= V \times 4 \times {10}^{-3}$
$\Rightarrow V= \dfrac {2}{4 \times {10}^{-3} }$
$\Rightarrow V= 0.5 \times {10}^{3}$
$\Rightarrow V= 500 V$

Thus, the potential difference between two points, if 2J of work must be done to move a 4 mC charge from one point to another is 500 V.

So, the correct answer is option B i.e. 500 V.

Note:
To solve these types of questions, students must have a clear knowledge about the concept of electrostatic force. Work done by a field in moving a charge from point to another is directly proportional to the change in the potential energy. Also, the work done by the force or the field on the charged particle will be independent of the path taken by the charge.