Question

Two point charges, \(+2\,\mu\text{C}\) and \(-2\,\mu\text{C}\), are fixed respectively at points \(A\) and \(B\), separated by \(4\,\text{m}\) in air. A point \(P\) is located such that it is \(3\,\text{m}\) from \(+2\,\mu\text{C}\) and \(5\,\text{m}\) from \(-2\,\mu\text{C}\). What is the electric potential at point \(P\)? \[ k=9\times10^9\,\text{N m}^2\text{C}^{-2} \]

• A. \(1.2\times10^3\,\text{V}\)
• B. \(2.4\times10^3\,\text{V}\)
• C. \(-3.6\times10^3\,\text{V}\)
• D. \(3.6\times10^3\,\text{V}\) \bigskip

Hint:

Electric potential is a scalar quantity, so potentials are added algebraically: \[ V=\sum \frac{kq_i}{r_i}. \] Positive charges contribute positive potential and negative charges contribute negative potential.

Answer 1

The Correct Option is B

Concept: Electric potential due to point charges: \(V = \sum kq/r\).

Step 1: \(V_1 = (9\times10^9)(2\times10^{-6})/3 = 6\times10^3\) V. \(V_2 = (9\times10^9)(-2\times10^{-6})/5 = -3.6\times10^3\) V. Total \(V = 2.4\times10^3\) V.

Step 2: Write the final answer. \(\boxed{V=2.4\times10^3\,\text{V}}\)