In the loops shown in fig. all curved section are either semicircles or quarter circles. All the loops carry same current. The magnetic fields at the centre have magnitudes `B_1, B_2,B_3 and B_4`. Then,

Options

A. `B_4` is maximum
B. `B_3` is minimum
C. `B_4gtB_1gtB_2gtB_3`
D. `B_1gtB_4gtB_3gtB_2`

Answer

A, B, C

Explanation

(a,b,c): For `B_1` and `B_4`, the contributions due to the different sect-
ions add up. For `B_2` and `B_3`, the contributions 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`. Fro `B_4`, there is a section with
radius ltb and hence, it contributes more than the semicircular
section of radius b for `B_1. Thus B_4gtB_1`.
for `B_3` , there is a section with radius gtb and hence it contributes
less than the semicircular section of radius b for `B_2`. Thus,`B_3ltB_2`.
Hence, `B_4gtB_1gtB_2gtB_3`