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Question

Two circular coils 1 and 2 are made from the same wire but the radius of 1st coil is twice that of the 2nd coil. What potential difference in volts should be applied across them so that the magnetic magnetic field at the centres is the same

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Solution

The correct option is **A** 4 times of first coil

Magnetic feild due to first coil and second coil is same at center.

Magnetic feild due to first coil and second coil is same at center.

Then magnetic field B at center is,

B=μ0I12(2r)=μ0I22(r)=I1I2=2 ..(1)

As we know that Resistance of coil is related as,

R=ρlA where ρ=resistivity ,l=length ,A=area of cross section.

ρ and A is same for both coil but l1=2π(2r) and l2=2π(r)

If V1 and V2 applied across first and second coil then,

I1=V1R1 and I2=V2R2

I1=V1ρl1A..(2) and I2=V2ρl2A ...(3)

From (1),(2),(3),

V1l1×l2V2=2

V1V1×l2l1=2

V1V2×12=2

V1V2=4

V1=4V2

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