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Question

Each of two long parallel wires carries a constant current i along the same direction.The wires are separated by a distance 2l.The magnitude of resultant magnetic induction in the symmetric plane of this system located between the wires at a distance R from each wire will be:

A
μ0iπR
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B
0
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C
μ0iπR2l2
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D
μ0iπR1l2R2
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Solution

The correct option is B 0
Let us consider a point P on the symmetric plane which is at distance R from the wires.
Using Amper's law,
B=μ0i2πR
Since the currents are equal and in the same direction, the magnetic field at P due to one will be equal and opposite to that due to other wire.
Hence, net magnetic field at P is zero.
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