Potential of a Cube

Electricity and Magnetism Level 4

Consider the potential $V$ and magnitude $E$ of an electric field at the vertex $P$ of a uniformly charged cube of side length $2s.$ Now, a cube of side length $s$ (also with $P$ as a vertex) is removed from the larger cube.

The new potential and magnitude of the electric field at $P$
are $\dfrac{V}{x}$ and $\dfrac{E}{y},$ respectively. What is $3xy?$

The answer is 8.

1 solution

Parnab Ghosh
May 5, 2018

Let charge on the cube is 8q.Electric field due to bigger cube at P is E=8kq/((s/√2)^2) and due to smaller cube removed is £=kq/((s/2√2)^2) since charge on smaller cube is q. Hence due remaining cube at P ,we will subtract the two fields which comes out to be E/2.Same technique to be used for potential also.

Potential of a Cube

The answer is 8.

1 solution

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