# A continuous line of charge lies along the x axis, extending from x = + x 0 to positive infinity. The line carries positive charge with a uniform linear charge density λ 0 . What are (a) the magnitude and (b) the direction of the electric field at the origin?

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 23, Problem 7P
Textbook Problem
652 views

## A continuous line of charge lies along the x axis, extending from x = +x0 to positive infinity. The line carries positive charge with a uniform linear charge density λ0. What are (a) the magnitude and (b) the direction of the electric field at the origin?

(a)

To determine

The magnitude of the electric field at the origin.

### Explanation of Solution

A continuous line of charge lies along the x-axis ranging from x=+x0 to x=+ and uniform linear charge density is λ0

General expression for magnitude of electric field due to small element of charge dq of length dx at point P.

dE=kedqx2                                                                                          (1)

Here, dE is the electric field, x is the distance from origin, dq is the electric charge and ke is the coulomb constant.

General expression for linear charge density is,

λ=qx

Rearrange the above equation

dq=λdx                                                                                                  (2)

Here, λ is the linear charge density, dq is element electric charge and dx is the elementary distance

(b)

To determine

The direction of electric field at the origin.

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