Q. 36

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Found in: Page 684

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# A hollow metal sphere has inner radiusand outer radius . The hollow sphere has charge. A point charge sits at the center of the hollow sphere.a. Determine the electric fields in the three regions ,, and .b. How much charge is on the inside surface of the hollow sphereOn the exterior surface

a.Three regions have electric fields,and .

b.There is electricity in the interior cavity isand the external surface is.

See the step by step solution

## Step 1: Calculation for electric field in (part a)

(a).

The electric flux is the quantity of electricity that flows through a closed surface.

Gauss's law states that the electric field passing through a surface is proportional to the charge within it.

The electric flux is,

For distance,the charge enclosed is.

Chargein the sphere is,

The area is,

.

So,

## Step 2: Calculation of electric field inandpart(a) solution

(a).

For distance is inside the conductor.

Inside the conductor, there is no electric field.

For distance ,

The charge enclosed is and.

So,

The area is,

.

## Step 3: Calculation for charge on the inner and outer surface of sphere (part b)

(b).

The cavity's positive charge causes a negative charge of the same magnitude on the cavity's inner surface.

As a result, the charge on the cavity's inner surface is the same magnitude as the charge within, but in the opposite direction.

Inner surface charge is,

The sphere has charge.

And the inner surface of the sphere has charge.

On the outside surface,

The total charge becomes,