A current loop, carrying a current of 5.0 A, is in the shape of a right triangle with sides 30,

step 1 Hello student here we have given a problem from chapter number 28 magnetic fields in this proble

A current loop, carrying a current of 5.0 A, is in the...

A current loop, carrying a current of $5.0 \mathrm{~A}$, is in the shape of a right triangle with sides 30,40 , and $50 \mathrm{~cm}$. The loop is in a uniform magnetic field of magnitude $80 \mathrm{mT}$ whose direction is parallel to the current in the $50 \mathrm{~cm}$ side of the loop. Find the magnitude of (a) the magnetic dipole moment of the loop and (b) the torque on the loop.

A current loop, carrying a current of $5.0 \mathrm{~A}$, is in the shape of a right triangle with sides 30,40 , and $50 \mathrm{~cm}$. The loop is in a uniform magnetic field of magnitude $80 \mathrm{mT}$ whose direction is parallel to the current in the $50 \mathrm{~cm}$ side of the loop. Find the magnitude of
(a) the magnetic dipole moment of the loop and
(b) the torque on the loop.

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Key Concepts

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity associated with a current loop, representing the strength and orientation of its magnetic field. It is calculated by multiplying the current flowing through the loop by the area enclosed by the loop, with the direction determined by the right?hand rule. This concept is fundamental in understanding how current loops interact with external magnetic fields.

Torque on a Current Loop

When a current loop is placed in a uniform magnetic field, it experiences a torque that tends to align its magnetic dipole moment with the field direction. The magnitude of this torque is given by the vector cross product between the magnetic dipole moment and the magnetic field, typically expressed as ? = ?B sin?, where ? is the angle between the dipole moment and the magnetic field. This principle is key to many magnetic devices and the analysis of magnetic materials.

Geometric Area Calculation

Determining the area enclosed by the current loop is essential for calculating the magnetic dipole moment. In many cases, including loops of various shapes, one must use geometric methods to compute the area accurately. This concept not only applies to triangles but to any planar shape, providing the necessary link between the geometric configuration of the loop and its magnetic properties.

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