Question

Two point charges \(q\) and \(-3q\) are kept 12 cm apart. The distance of the point from \(q\) on the line between two charges at which potential due to this system of charges is zero will be:

• A. 6 cm
• B. 4 cm
• C. 3 cm
• D. 2 cm

Hint:

When dealing with the potential of point charges, remember that the potential is a scalar quantity. Therefore, to find the point of zero potential, we set the magnitudes of the potentials equal and solve for the distance.

Answer 1

The Correct Option is B

Let the distance between the charge \(q\) and the point where the potential is zero be \(x\). The distance between the point and the charge \(-3q\) will be \(12 - x\). The potential at a point due to a point charge is given by the formula: \[ V = \frac{kQ}{r} \] where \(k\) is the electrostatic constant, \(Q\) is the charge, and \(r\) is the distance from the charge. For the potential to be zero, the potentials due to both charges must be equal in magnitude and opposite in sign. Hence, we have: \[ \frac{kq}{x} = \frac{k(3q)}{12 - x} \] Simplifying the equation: \[ \frac{1}{x} = \frac{3}{12 - x} \] Cross multiplying: \[ 12 - x = 3x \] \[ 12 = 4x \] \[ x = 3 \, \text{cm} \] Thus, the point at which the potential is zero is 4 cm from the charge \(q\).