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In the loops shown in fig. all curved se...

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,

A

`B_4` is maximum

B

`B_3` is minimum

C

`B_4gtB_1gtB_2gtB_3`

D

`B_1gtB_4gtB_3gtB_2`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
(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`
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Knowledge Check

  • In the loop 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) (i) B_(4) is maximum (ii) B_(3) is minimum (iii) B_(4)gtB_(1)gtB_(2)gtB_(3) (iv) B_(1)gtB_(4)gtB_(3)gtB_(2)

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    (ii),(iii)
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