Question

• Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in figure. Each carries current out of the plane of paper. Axis is at a distance R from each wire.

What will be the field if current in one of the wires (say A) is switched off?

Answer 1

Given, current carried by each wire = I

As all the wires are equidistant from point O, and are in the same plane

So, magnetic field at point O

${\overrightarrow{B}}_{net}=0$
${\overrightarrow{B}}_A+{\overrightarrow{B}}_{\text{by other four}}=0$

If current in one of the wires (say A) is switched off

${\overrightarrow{B}}_{\text{by other four}}=-{\overrightarrow{B}}_A$

Where, From right hand rule
${\overrightarrow{B}}_A=\frac{{\mu }_{0}i}{2\pi R}\left(\hat{i}\right)$

Then
${\overrightarrow{B}}_{\text{by other four}}=\frac{{\mu }_{0}i}{2\pi R}(-\hat{i})$
Perpendicular to AO towards left.

Final Answer:
$\frac{{\mu }_{0}i}{2\pi R}$ (perpendicular to AO towards left)