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If the resistance of the upper half of a...

If the resistance of the upper half of a rigid loop is twice of that of the lower half, the magnitude of magnetic induction at the centre is eual to

A

zero

B

`(mu_0 I)/(12 a)`

C

`(mu_0 I)/(2 a)`

D

`(mu_0 I)/(3a)`

Text Solution

Verified by Experts

The correct Answer is:
b
`because I_1 R_1 = I_2R_2`
`therefore (I_1)/(I_2) = (R_2)/(R_1) = (R_2)/(2R_2) = 1/2`
or `I_2 = 2I_1`

Also, `I = I_1 + I_2`
`= I_1 + 2I_1 = 3I_1`
`therefore I_1 = I/3`
and `I_2 = (2I)/3`
Magnetic field at the centre of the coil is,
`vecB_0 = B_1 ox + B_2 o.`
or `B_0 = (mu_0 I_1 pi)/(4pi a) + (mu_0 I_2 pi)/(4 pi a) ` or
`B_0 = (mu_0 pi)/(4 pi a) (I_2 - I_1)`
` = (mu_0)/(4a) ((2I)/(3) - I/3)`
`= (mu_0)/(4a)(I/3)`
or `B_0 = (mu_0 I)/(12 a)`
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