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Q. 42

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A positive point charge sits at the center of a hollow spherical shell. The shell, with radius and negligible thickness, has net charge . Find an expression for the electric field strength (a) inside the sphere, , and (b) outside the sphere, . In what direction does the electric field point in each case?

a.Expression for the electric field isand the direction is outward.

b.Expression for the electric field is and the direction is inward the sphere.

See the step by step solution

Step by Step Solution

Step 1: Formula for electric flux

Electric flux,

Step 2: Expression for electric field and direction at (part a)

(a).

Assume

For distance (inside the sphere):

The charge enclosed is .

So,

The gaussian surface's area is.

Substitute all values in equation 1,

We get,

Because the electric field points outward from the positive charge, the electric field's direction is outward from the sphere.

Step 3: Expression for electric field and direction at (part b)

(b).

Assume

For distance (outside the sphere):

The charge enclosed is and .

So,

The gaussian surface's area is .

Substitute all values in equation,

We get,

The electric field is directed inward the sphere because it is directed inward the negative charge.

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