Question

A solid non-conducting cube of side length a is uniformly charged with density ρ. If the potential at corner of cube is V, then potential at its centre will be nV. Find value of n.

Answer 1

Answer:

answer is 02.00

Explanation:

Answer 2

The potential at the corner of a solid non-conducting cube is V and the potential at the centre is nV. Here n is 2.

Given:

The non-conducting cube has a side length 'a'.

The cube is uniformly charged with charge density $\rho$.

The potential at the corner of the cube = V

The potential at its centre = nV

To Find:

The value of n.

Solution:

The Potential is directly proportional to the unit charge (Q) and inversely proportional to the side of the cube.

Potential ∝ $\frac{Q}{a}$

and, Q= $\rho$×a³

So, potential ∝ $\frac{\rho a^3}{a}$

Potential ∝ a² [ $\rho$ is constant]

Here we can solve it by superposition.

With the 8 small cubes, we can make another cube.

The side length of the big cube is 2a.

Now the potential at the centre of this new larger cube is 8 times the potential at the corner of each of the smaller cubes if they are isolated.

The potential at the centre of the big cube is 8V.

Potential at the corner of big cube = V× 2²= 4V

The ratio of the electrostatic potential at the centre of the cube to that at one of the corners of the cube is 8V: 4V= 2: 1

So, the value of n will be 2.

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