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Q. 47

Expert-verified
Found in: Page 655

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

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

# Charge Q is uniformly distributed along a thin, flexible rod of length L. The rod is then bent into the semicircle shown in FIGURE. 23.47a. Find an expression for the electric field at the center of the semicircle.Hint: A small piece of arc length spans a small angle , where is the radius.b. Evaluate the field strength if and .

(a) Electrical field at the center of the semicircle is ,

(b) Field strength, when is

See the step by step solution

## Step1: Introduction

The existence of a charged object affects the realm around it, causing an electrical field to create therein space. A charged object produces an electrical field, which could a change within the space or field surrounding it. The extraordinary modification of the realm would be felt by other charges in this field.

Small angle,

Angle,

Length,

Charge,

## Step2: Find Electrical field (part a)

CALC Charge Q is evenly distributed throughout the length L of a thin, flexible rod. Figure shows how the rod is bent into a semicircle. Graph Cenier

a. Find the following expression for the electric field E at the semicircle's centre: As spans a little angle, a small amount of arc length , where R denotes the radius of the circle. .

and , then

Integrate equations, to

Imposing restrictions to the magnitude of the electrical field,

## Step3: Find field intensity (part b)

If and , calculate the field strength.

, then

Given and charge , solve equation