Question

A point charge +Q is placed at the origin. The electric potential at point (3a,4a,0) in terms of k, Q and a is:

• A. kQ/5a
• B. kQ/3a
• C. kQ/7a
• D. kQ/2a

Hint:

Electric potential is a scalar quantity, so you only need the magnitude of the distance between the charge and the point of interest. Remember the 3-4-5 right triangle, as it frequently appears in physics problems to simplify distance calculations.

Answer 1

The Correct Option is A

Step 1: Recall the formula for the electric potential of a point charge. The electric potential \(V\) at a distance \(r\) from a point charge \(Q\) is given by: \[ V = \frac{kQ}{r} \] where \(k = \frac{1}{4\pi\epsilon_0}\) is Coulomb's constant.
Step 2: Calculate the distance \(r\) from the origin to the given point. The charge is at the origin (0,0,0) and the point is at (3a,4a,0). The distance \(r\) is the magnitude of the position vector, calculated using the distance formula in 3D: \[ r = \sqrt{(3a-0)^2 + (4a-0)^2 + (0-0)^2} \] \[ r = \sqrt{(3a)^2 + (4a)^2} = \sqrt{9a^2 + 16a^2} = \sqrt{25a^2} = 5a \]
Step 3: Substitute the distance \(r\) into the potential formula. \[ V = \frac{kQ}{5a} \]