MHT-CET Physics Electrostatics PYQ - Work Done Problem

2) 90 J of work is done to move an electric charge of magnitude \(3\text{ C}\) from a place A, where the potential is \(-10\text{ V}\), to another point B where the potential is \(V_1\) Volt. What is the value of \(V_1\)?

A. \( 10\text{ V} \)

B. \( 20\text{ V} \)

C. \( 30\text{ V} \)

D. \( -40\text{ V} \)

Solution:

The work done \(W\) to move a charge \(q\) from potential \(V_A\) to \(V_B\) is given by: \[ W = q \times (V_B - V_A). \] Here, \(W = 90\text{ J}\), \(q = 3\text{ C}\), and \(V_A = -10\text{ V}\). Let \(V_B = V_1\). Thus: \[ 90 = 3 \times (V_1 - (-10)) = 3 \times (V_1 + 10). \] Dividing both sides by 3: \[ 30 = V_1 + 10 \quad \Longrightarrow \quad V_1 = 20\text{ V}. \] Hence, option B is the correct answer.