A circular loop of wire of area 10 cm^2 carries a current of 25 A. At a particular instant, the

step 1 We have diple moment mu equals iA equals negative 25 amp times 10 to the minus 3 meter square j

A circular loop of wire of area 10 cm^2 carries a current of...

A circular loop of wire of area $10 \mathrm{cm}^{2}$ carries a current of 25 A. At a particular instant, the loop lies in the $x y$ -plane and is subjected to a magnetic field $$\overrightarrow{\mathbf{B}}=(2.0 \hat{\mathbf{i}}+6.0 \hat{\mathbf{j}}+8.0 \hat{\mathbf{k}}) \times 10^{-3} \mathrm{T} . \quad \text { As } \quad \text { viewed }$$ from above the $x y$ -plane, the current is circulating clockwise. (a) What is the magnetic dipole moment of the current loop? (b) At this instant, what is the magnetic torque on the loop?

Key Concepts

Area Vector

The area vector is a vector whose magnitude equals the area of a surface and whose direction is perpendicular to that surface. In current loops, the area vector is used to determine the direction of the magnetic dipole moment based on the right?hand rule. This concept is essential for linking geometric orientation with magnetic properties in physical systems.

Cross Product

The cross product is a mathematical operation that takes two vectors and produces a new vector that is perpendicular to the plane of the original vectors. Its magnitude is determined by the product of the magnitudes of the two vectors and the sine of the angle between them. In the context of magnetic interactions, it is used to calculate torques and other quantities where direction and perpendicularity are key.

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity that represents the strength and orientation of a magnet or current loop in a magnetic field. It is defined for a current loop as the product of the current and the area vector, whose direction is determined by the right?hand rule. This concept is crucial in understanding how current loops interact with external magnetic fields, influencing both energy and torque.

Magnetic Torque

Magnetic torque is the twisting force experienced by a magnetic dipole when subjected to an external magnetic field. It is given by the vector cross product of the magnetic dipole moment and the magnetic field, resulting in a torque that tends to align the dipole with the magnetic field. This concept is important for analyzing the rotational effects and stability of magnetic systems.

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