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Question

# A long, straight wire, of radius a, carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire, at distances a3 and 2a, respectively from the axis of the wire, is:

A
23
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B
2
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C
12
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D
32
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Solution

## The correct option is A 23Let a be the radius of the wire. Magnetic field at point A (inside the wire): BA=μ0ir2πa2=μ0i(a3)2πa2=μ0i6πa Magnetic field at point B (outside the wire): BB=μ0i2π(2a)=μ0i4πa ∴BABB=(μ0i6πa)(μ0i4πa)=46=23 Hence, (A) is the correct answer.

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