Question

If four charges \( q_1 = +1 \times 10^{-8} C \), \( q_2 = -2 \times 10^{-8} C \), \( q_3 = +3 \times 10^{-8} C \), and \( q_4 = +2 \times 10^{-8} C \) are kept at the four corners of a square of side 1 m, then the electric potential at the centre of the square is:

• A. \( 300 \) V
• B. \( 200 \) V
• C. \( 510 \) V
• D. \( 410 \) V

Hint:

The electric potential due to multiple charges is algebraic sum because potential is a scalar quantity. Use \( V = \frac{kq}{r} \) for each charge and sum them.

Answer 1

The Correct Option is C

Step 1: Using the Formula for Electric Potential The electric potential at the center due to a charge \( q \) placed at a distance \( r \) is given by: \[ V = \frac{kq}{r}. \] Since all four charges are at the same distance \( r = \frac{1}{\sqrt{2}} \) m from the center, the total potential is: \[ V_{\text{total}} = k \left( \frac{q_1 + q_2 + q_3 + q_4}{r} \right). \]
Step 2: Substituting Values \[ V_{\text{total}} = 9 \times 10^9 \times \left( \frac{(1 - 2 + 3 + 2) \times 10^{-8}}{1/\sqrt{2}} \right). \] \[ V_{\text{total}} = 9 \times 10^9 \times \left( \frac{4 \times 10^{-8}}{1/\sqrt{2}} \right). \] \[ V_{\text{total}} = 510 V. \] Thus, the correct answer is: \[ \boxed{510 \text{ V}}. \]