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Question

# A moving charge can produce a magnetic field. How does a current loop behaves like a magnetic dipole?

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Solution

## When an electric current flows in a closed loop of wire, placed in a uniform magnetic field, the magnetic forces produce a torque which tends to rotate the loop so that area of the loop is perpendicular to the direction of the magnetic field.Consider a rectangular coil PQRS placed in an external magnetic field as shown in diagram (a). Let ′I′ be the current flowing through the coil. Each part of the coil experiences one Lorentz. Each part of the forces is→F1, →F2, →F3 and →F4 as shown. The forces are equal in magnitude but act in opposite directions along the same straight line. Hence they cancel outThe force →F1=I(→PQ×→B)F1=IlB when θ=900 →F1 acts in direction perpendicular to the plane of paper.Similarly, →F3=I(→RS×→BF3=IB when θ=900The two forces constitute a couple and so rotates the coil in the anticlockwise. The torque is given by τ= force x arm of couple τ=Fbcosθτ=IlB bcosθτ=IABcosθThe area vector A makes an angle α with the →B so θ+α=900cosθ=cos(90−α)=sinα∴τ=NIAB sinατ=PmB sinα→τ=→Pm×→B where Pm=NIA called the magnetic dipole moment of the loop.

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