Question

In the loops shown in the figure, all curved section 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 $B_4$ respectively. Then,

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

Answer 1

Answer: (A), (C)

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

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