Question

In the loops shown in figure 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 $B_4$:

• 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 $B_4>B_1>B_2>B_3$

The direction of current are shown in the figure. The magnetic field due to a current carrying wire is inversely proportional to the distance of the wire from the point. For B4 the current in the loop flows in the same direction with respect to the center. Again the part p is nearer to the center. So B4 has a largest field at the center. Now for B1, all the things are almost same as B4 except the part p. So B1 comes second. Now for B2 and B3 the current flowing through two segments are in opposite direction. But they are in a different distance from the center. Again B3 has an another part q which is a a far distance respective to its adjacent part. For this B3 end up with a minimum field.