Q. 42

Expert-verifiedFound in: Page 685

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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.

Electric flux,

(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.

(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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