Question

What is the magnetic field at 0 due to current in the infinite wire forming a loop as shown in the following figure?

• A. $\frac{\mu_{0} I}{4 \pi d}\left(\cos \phi_{1}+\cos \phi_{2}\right)$
• B. $\frac{\mu_{0}}{4 \pi} \times \frac{2 l}{d}$
• C. $\frac{\mu_{0} I}{4 \pi d}\left(\sin \phi_{1}+\sin \phi_{2}\right)$
• D. $\frac{\mu_{0}}{4 \pi} \times \frac{I}{d}$

Answer 1

Answer: (A)

Here, required angles $\theta_{1}$ and $\theta_{2}$
are $\left(90^{\circ}-\phi_{1}\right)$ an
$\left(90^{\circ}-\phi_{2}\right)$
$\therefore B =\frac{\mu_{0} I}{4 \pi d}\left[\sin \left(90^{\circ}-\phi_{1}\right)+\sin \left(90^{\circ}-\phi_{2}\right)\right]$
$=\frac{\mu_{0} I}{4 \pi d}\left[\cos \phi_{1}+\cos \phi_{2}\right]$