IGNOU MPH 3 2026 - An infinite plane conducting surface is held at zero potential. A poin

Question

An infinite plane conducting surface is held at zero potential. A point charge q is placed at a distance d above the plane. Using the method of images,

19 Jan 2026

Answer :

Word Count : 314

Consider a point charge (q) at a distance (d) above an infinite grounded conducting plane. By the method of images, we replace the conducting plane with an image charge (-q) located a distance (d) below the plane, at the mirror position. The potential at any point above the plane is then equivalent to that produced by the two charges (q) at ((0,0,d)) and (-q) at ((0,0,-d)) in free space. The potential at a point ((x,y,z)) above the plane is [ V(x,y,z) = \frac{1}{4 \pi \varepsilon_0} \left[ \frac{q}{\sqrt{x^2 + y^2 + (z-d)^2}} - \frac{q}{\sqrt{x^2 + y^2 + (z+d)^2}} \right]. ] The induced surface charge density (\sigma(x,y)) on the plane (z=0) is given by [ \sigma(x,y) = -\varepsilon_0

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