A circular coil of 100 turns and effective diameter 20 cm carries a current of 0.5 A. It is to

step 1 In this problem, work done is given by mb cost theta 1 minus mb cost theta 2. So putting the val

A circular coil of 100 turns and effective diameter 20 cm...

A circular coil of 100 turns and effective diameter $20 \mathrm{~cm}$ carries a current of $0.5 \mathrm{~A}$. It is to be turned in a magnetic field $B=2 T$ from a position in which $\theta$ equals zero to one in which $\theta$ equals $180^{\circ}$. The work required in this process is: (a) $\pi$ joule (b) $2 \pi$ joule (c) $4 \pi$ joule (d) $8 \pi$ joule

A circular coil of 100 turns and effective diameter $20 \mathrm{~cm}$ carries a current of $0.5 \mathrm{~A}$. It is to be turned in a magnetic field $B=2 T$ from a position in which $\theta$ equals zero to one in which $\theta$ equals $180^{\circ}$. The work required in this process is:
(a) $\pi$ joule
(b) $2 \pi$ joule
(c) $4 \pi$ joule
(d) $8 \pi$ joule

Key Concepts

Magnetic Dipole Moment

This refers to the quantity that represents the effectiveness of a current loop in generating a magnetic field. It is calculated as the product of the current, the number of turns in the coil, and the area enclosed by the loop. It plays a key role in determining how the coil interacts with an external magnetic field.

Torque on a Current Loop

A current loop in a magnetic field experiences a torque, which is given by the cross product of its magnetic dipole moment and the magnetic field. This torque tends to rotate the coil such that its dipole moment aligns with the field, and the magnitude of the torque depends on both the magnetic field strength and the sine of the angle between the dipole moment and the field.

Magnetic Potential Energy

The magnetic potential energy of a dipole in a magnetic field is defined as the negative of the dot product of its magnetic dipole moment and the magnetic field. This energy quantifies the stability of the dipole's orientation within the field, with the lowest energy state achieved when the dipole is aligned with the field.

Work Done in Rotating a Coil

As the coil is rotated within a magnetic field, work is done against the magnetic torque, which corresponds to the change in magnetic potential energy. The work required to change the coil's orientation can be calculated by taking the difference in potential energy between the initial and final positions.

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