Question

In the loops shown, all curved sections are either semicircles or quarter circles. All the loops carry the same current. The magnetic fields at the centres have magnitudes $B_1,B_2,B_3$ and $B_4$ :
Assume the current to be in clockwise direction in the semicircle of radius a.

• A. $B_4$ is maximum
• B. $B_3$ is minimum
• C. $B_4>B_1>B_2>B_3$
• D. $B_1>B_4>B_3>B_2$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $B_4$ is maximum
B $B_3$ is minimum
C $B_4>B_1>B_2>B_3$

For $B_1$ and $B_4$ the contribution due to the different sections add up. For $B_2$ and $B_3$, the contribution due to the outer sections oppose the contributions due to the inner sections. thus, $B_1$ and $B_4$ are greater than $B_2$ and $B_3$ for $B_4$ , there is a section with radius < b and hence , it contributes more than the semicircular section of radius b for $B_1$ thus, $B_4>B_1$
For $B_3$ there is section with radius > b and hence it contributes less than semicircular section of radius b for $B_2$ thus. $B_3<B_2$.
Hence , $B_4>B_1>B_2>B_3$