Q. 43

Expert-verifiedFound in: Page 655

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

FIGURE shows a thin rod of length with total charge .

a. Find an expression for the electric field strength at point on the axis of the rod at distance from the center.

b. Verify that your expression has the expected behavior if .

c. Evaluate at if and .

Part

The expression for the electrical field,

Part

The expression reduces to the expression for the point charge,

Part

The field strength is

As illustrated in the illustration, move the axis all along rod with origin at the end. The linear charge density is calculated as follows:

It has a charging aspect to it.

Because the wire section is so small, it can be viewed as a point charge. As a result, the field element produced just at point away from the wire along the axis is given by

The equation is integrated as,

Remove everything in integral that is constant.

Denote,

Introduce a substitution,

The new integration bounds are

In this case, then can be neglected by . so,

This turns out to be an expression for the expected charge far away from the point; the entire wire appears to be a point charge.

The vector sum of all forces exerted by a field at a particular position within the field on a unit mass, unit charges, unit magnetic pole, and so on from the figure as

(constant)

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