Question

A uniformly changed wire is bent in the form of circle, of radius $a$. If charge per unit length is $\lambda \text{C/m}$, the electric field at the centre $O$ is,

• A. $\frac{\lambda }{\pi a{\in }_0}$
• B. $\frac{\lambda }{4\pi a{\in }_0}$
• C. Zero
• D. $\frac{\lambda }{2\pi {\in }_{0}a}$

Answer 1

The correct option is C Zero


If we take a small strip of the circular wire at point $A$, then the electric field due to it at centre $O$, is shown in the figure.
For this strip, there is another small strip diametrically opposite to it, at $B$, whose electric field at centre $O$ is also shown in the figure.
By symmetry, these two fields will cancel out each other.
Hence, the net electric field will be zero.
For every strip on the circular wire, there is a diametrically opposite strip which cancel the fields of each other.
Thus, the net electric field at the centre of the circular wire will always be zero.

Hence, $\left(C\right)$ is the correct answer.