A wire of length L is bent in the form of a circular coil of some turns. A current I flows through the coil. The coil is placed in a uniform magnetic field B. The maximum torque on the coil can be

Question

A wire of length L is bent in the form of a circular coil of some turns. A current I flows through the coil. The coil is placed in a uniform magnetic field B. The maximum torque on the coil can be (A) (IBL2/2π) (B) (IBL2/4π) (C) (IBL2/π) (D) (2IBL2/π)

Tardigrade Admin · Accepted Answer

Let r be the radius of the coil and n be the number of turns formed. Then L = 2 π r n or r = (L/2 π n) ....(i) Maximum torque, τmax = B n IA = B n I π r2 = B n I π × (L2/4 π2 n2) = (B IL2/4 π n) Torque will be maximum if n = 1 ∴ : :: :: τmax = (B I L2/4 π)

Q. A wire of length $L$ is bent in the form of a circular coil of some turns. A current $I$ flows through the coil. The coil is placed in a uniform magnetic field $B$ . The maximum torque on the coil can be

$\frac{I B L ^{2}}{2 π}$

$\frac{I B L ^{2}}{4 π}$

$\frac{I B L ^{2}}{π}$

$\frac{2 I B L ^{2}}{π}$

Q. A wire of length L is bent in the form of a circular coil of some turns. A current I flows through the coil. The coil is placed in a uniform magnetic field B. The maximum torque on the coil can be

2πIBL2​

4πIBL2​

πIBL2​

π2IBL2​

Let r be the radius of the coil and n be the number of turns formed. Then L=2πrn or r=2πnL​ ....(i) Maximum torque, τmax​=BnIA=BnIπr2 =BnIπ×4π2n2L2​=4πnBIL2​ Torque will be maximum if n=1 ∴τmax​=4πBIL2​

Q. A wire of length $L$ is bent in the form of a circular coil of some turns. A current $I$ flows through the coil. The coil is placed in a uniform magnetic field $B$ . The maximum torque on the coil can be

$\frac{I B L ^{2}}{2 π}$

$\frac{I B L ^{2}}{4 π}$

$\frac{I B L ^{2}}{π}$

$\frac{2 I B L ^{2}}{π}$