Question 45: Magnetism and Matter

Question

An infinite wire has a circular bend of radius
a
, and carrying a current
I
as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m6rjvdwl/bccbe477-401f-4c30-be85-4b8c4eca78ba/93af5550-e38d-11ef-9897-61eb62716c5d/file-jaoe38c1m6rjvdwm.png?format=png)

Accepted Answer

$\begin{aligned}
& \mathrm{B}_1=\frac{\mu_0 \mathrm{i}}{4 \pi \mathrm{a}} \otimes \
& \mathrm{~B}_2=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}}{\mathrm{a}}\left(\frac{3 \pi}{2}ight) \otimes \
& \mathrm{B}_3=0 \
& \mathrm{~B}=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}}{\mathrm{a}}\left(1 \frac{3 \pi}{2}ight) \otimes
\end{aligned}$
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m74pjn58/18601f2f-6e70-4781-bda2-bafb3798408c/f45482c0-eac9-11ef-be87-1347496dd836/file-jaoe38c1m74pjn59.png?format=png)

Answer

$\frac{\mu_0}{2 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+2\right]$

Answer

$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+1\right]$

Answer

$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{\pi}{2}+1\right]$

Answer

$\frac{\mu_0}{4 \pi} \frac{\mathrm{I}}{\mathrm{a}}\left[\frac{3 \pi}{2}+2\right]$

Magnetism and Matter

An infinite wire has a circular bend of radius a , and carrying a current I as shown in the figure. The magnitude of magnetic field at the origin O of the arc is given by:

Choose the correct answer: