A wire carrying current i has the configuration shown in figure. For B to be zero at the centre of the circle, $θ$ must be-

Question

A wire carrying current i has the configuration shown in figure. For B to be zero at the centre of the circle, θ must be-

TestHub · Accepted Answer

To have zero magnetic field at the center, the field due to the circular arc must cancel the field due to the straight wire.

The magnetic field at the center of a circular arc is $B_{a rc} = \frac{μ _{0} I}{4 π R} θ$ .

The magnetic field due to a semi-infinite straight wire is $B_{w i re} = \frac{μ _{0} I}{4 π R}$ .

For $B_{t o t a l} = 0$ , we need $B_{a rc} = B_{w i re}$ .

So, $\frac{μ _{0} I}{4 π R} θ = 2 (\frac{μ _{0} I}{4 π R})$ .

This implies $θ = 2$ radian.

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