   Chapter 15.3, Problem 15.4QQ

Chapter
Section
Textbook Problem

A circular ring of charge of radius b has a total charge q uniformly distributed around it. Find the magnitude of the electric field in the center of the ring.(a) 0 (b) keq/b2 (c) keq2/b2 (d) keq2/b (e) None of these answers is correct.

To determine
The electric field at the centre of the ring.

Explanation

The circular ring can be divided in to n number of segments. Each segment contributes to the force at the centre. But, for the force due to every segment, there will be a force due to the diametrically opposite segment which is equal and opposite. Therefore, the net force at the centre is zero.

Conclusion:

The electric field at the centre is given by,

E=Fq

• F is the net force.
• q is the charge.

Since, the net force is zero, the electric field is also zero at the centre. Thus, option (a) is correct.

The quantity keq/b2 represents the electric field due to a single charge at the centre

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