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Question

# Two current-carrying parallel conductors are shown in the figure. The magnitude and nature of force acting between them per unit length will be :

A
8×108N/m, attractive
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B
3.2×105N/m, repulsive
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C
3.2×105N/m, attractive
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D
8×108N/m, repulsive
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Solution

## The correct option is C 3.2×10−5N/m, attractiveForce on a current carrying conductor is F=∫i(→dl×→B)Magnetic field due to one wire at the location of the second wire ( other one ) is B1=μ0i12πdForce on the 2nd wire due to B1 is F21=i2l2B1=i2l2μ0i12πd=μ0i1i2l22πdForce per unit length for wire l2 is Fperunitlength=F21l2=μ0i1i22πd=2×10−7×4×410×10−2=3.2×10−5Nwhere F21 is the force on wire 2 due to wire 1 and the subscript 2 refers to 2nd wire.B1 is in −^k direction.l2 is in −^j direction.Hence, F21 will be in ^j×(−^k)=−^i direction.Similarly, F12 will be in ^i direction.Thus, both the wires will attract each other.

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