Question

Define the magnetic moment of a current-carrying coil. Write its SI unit.

Hint:

The magnetic moment is a vector quantity, pointing normal to the plane of the coil, and it depends on both the current and the area of the coil.

Answer 1

1. Magnetic Moment of a Current-Carrying Coil:

The magnetic moment (\( \mu \)) of a current-carrying coil is a vector quantity that represents the strength and orientation of the coil's magnetic field. It is defined as the product of the current \( I \) flowing through the coil and the area \( A \) of the coil, along with the direction normal to the plane of the coil (perpendicular to the coil's surface).

The formula for the magnetic moment of a coil is given by:

\[ \mu = I \cdot A \]

Where:

• \( I \) is the current flowing through the coil (in amperes, A).
• \( A \) is the area of the coil (in square meters, m²).

2. Direction of Magnetic Moment:

The direction of the magnetic moment vector is determined by the right-hand rule. If the fingers of the right hand curl in the direction of the current, then the thumb points in the direction of the magnetic moment.

3. SI Unit of Magnetic Moment:

The SI unit of magnetic moment is the ampere-square meter (A·m²), which is derived from the current \( I \) in amperes and the area \( A \) in square meters.

4. Conclusion:

• The magnetic moment of a current-carrying coil is \( \mu = I \cdot A \).
• The SI unit of magnetic moment is ampere-square meter (A·m²).