Question

Two points R and S are equidistant from two charges \( +Q \) and \( -2Q \). The work done in moving a charge \( -Q \) from point R to S is:

• A. Zero
• B. \( - \frac{Q}{4 \pi \epsilon_0 d} \)
• C. \( \frac{Q}{4 \pi \epsilon_0 d} \)
• D. \( \frac{3Q}{4 \pi \epsilon_0 d} \)

Hint:

When moving a charge between two points where the electric potential is the same, no work is done since the potential difference \( \Delta V = 0 \).

Answer 1

The Correct Option is A

The electric potential at any point due to a point charge is given by: \[ V = \frac{1}{4 \pi \epsilon_0} \frac{Q}{r} \] where \( Q \) is the charge and \( r \) is the distance from the charge. Since points R and S are equidistant from the two charges \( +Q \) and \( -2Q \), the potential at these points due to each charge will be the same. Therefore, the net potential at both points will be equal, and as a result, the work done in moving the charge \( -Q \) from point R to point S will be zero, since work is given by \( W = q \Delta V \), and \( \Delta V = 0 \). Final Answer: (A) Zero