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Question -

(a) Acircular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A issuspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T.The field lines make an angle of 60º with the normal of the coil. Calculate themagnitude of the counter torque that must be applied to prevent the coil fromturning.

(b) Wouldyour answer change, if the circular coil in (a) were replaced by a planar coilof some irregular shape that encloses the same area? (All other particulars arealso unaltered.)



Answer -

(a) Numberof turns on the circular coil, n = 30

Radius of the coil, r =8.0 cm = 0.08 m

Area of the coil 

Current flowing in thecoil, I = 6.0 A

Magnetic field strength, B =1 T

Angle between the field lines andnormal with the coil surface,

θ =60°

The coil experiences a torque inthe magnetic field. Hence, it turns. The counter torque applied to prevent thecoil from turning is given by the relation,

τ = n IBA sinθ …(i)

= 30 × 6 × 1 × 0.0201 × sin60°

= 3.133 N m

(b) Itcan be inferred from relation (i) that the magnitude of the appliedtorque is not dependent on the shape of the coil. It depends on the area of thecoil. Hence, the answer would not change if the circular coil in the above caseis replaced by a planar coil of some irregular shape that encloses the samearea.

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