Ncert Exercises & Solutions

32. Two charges $q_{1}$ and $q_{2}$ are placed at (0, 0, d) and (0, 0, -d) respectively. Find the locus of points where the potential is zero.

NEETprep Answer:

Hint: The sum of the potential due to both charges will be equal to zero.

Let any arbitrary point on the required plane is (x, y, z). The two charges lie on the z-axis at a separation of 2d.

Step 1: Find the net potential at the point and make it equal to zero.

The potential at the point P due to two charges is given by:

\frac{q_{1}}{\sqrt{x^{2} + y^{2} + {(z - d)}^{2}}} + \frac{q_{2}}{\sqrt{x^{2} + y^{2} + {(z + d)}^{2}}} = 0

\frac{q_{1}}{\sqrt{x^{2} + y^{2} + {(z - d)}^{2}}} = \frac{- q_{2}}{\sqrt{x^{2} + y^{2} + {(z + d)}^{2}}}

On squaring and simplifying, we get,

x^{2} + y^{2} + z^{2} + [\frac{{(\frac{q_{1}}{q_{2}})}^{2} + 1}{(q)}] \times (2 zd) + d^{2} = 0

This is the equation of a sphere with a centre at

(0, 0, - 2 d [\frac{{q_{1}}^{2} + {q_{2}}^{2}}{{q_{1}}^{2} - {q_{2}}^{2}}])