Question

Two concentric circular loops of radii 0.08m and 0.1m carry current such that magnetic field at the centre is zero if the current in the outer loop is 8A clockwise, current in the inner loop is:
a. 6.4a anticlockwise
b. 6.4a clockwise
c. 8a anti-clockwise
d. 3.2a clockwise

I want answer with full solution as soon as possible.

Answer 1

The current in the inner loop is 6.4 a anticlockwise.

Explanation:

We are given

• R1 = 0.1 m
• R2=0.08 m
• I1 = 8A

Magnetic field at centre O due to current in outer loop, B1 = μ0I1 / 2R1  

Let the current in inner loop be I2 and magnetic field at centre O due to it be B2

As B1+B2 or B1 = −B2

I2 must be anti-clockwise and B1 = B 2

OR

μ0I1 / 2R1 = u0I2 / 2R2

I2 = I1  / R1 × R2 = 8 / 0.1 × 0.08  

= 6.4 A

Hence the current in the inner loop is 6.4 a anticlockwise.

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