 # Current-Carrying Coil in an External Magnetic Field

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This Demonstration shows the motion of a current-carrying coil placed in an external magnetic field. The coil behaves as a magnetic dipole and so experiences a torque in the presence of an external magnetic field. We consider two scenarios.

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In the "fixed coil" case, you can modify specific characteristics of the coil (length, height, radius, number of loops and current), the strength of the external magnetic field and the initial angle between the magnetic dipole moment and the external field. This scenario shows an energy-versus-angle plot with a red dot located at the initial angle. On the right side, you can see the value of the dipole moment of the coil, its magnetic field and the module of the torque it experiences. On the left side, you can see the coil, the direction of its current and the direction of the vectors of external magnetic field, dipole moment and torque.

In the "moving coil" case, when you press animate, the coil moves in response to the torque it experiences. The energy plot then shows the conservation of energy in the coil–field system.

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Contributed by: Fis. Fernando Moncada and Telmo Aguilar (June 2021)
Suggested by: Esteban Irribarra
(Developed in the Physics Laboratory of Escuela Politécnica Nacional)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

The magnetic field produced by a large current-carrying coil is obtained by Ampere's law. Inside the coil it is given by: ,

where is the vacuum magnetic permeability, is the density of loops, is the total number of loops, is the length of the coil and is the magnitude of its current.

A loop that carries a magnetic field has a magnetic dipole moment. A small coil of loops has the approximate magnetic dipole moment given by: ,

where is the area of the loop and is its radius. The magnetic dipole moment is a vector and its direction is given by the right-hand rule according to the direction in which the current is flowing. If the current is counterclockwise, the dipole moment is directed upward, and if the current is clockwise, the dipole moment is directed downward.

A magnetic dipole moment in the presence of an external magnetic field experiences a torque given by .

A magnetic dipole also stores energy in the presence of an external field. Its potential energy is given by .

A dipole in an external field experiences a torque that makes it rotate. When it rotates, it transforms part of its potential energy into kinetic energy maintaining its total energy constant, according to the conservation of energy law: .

## Permanent Citation

Fis. Fernando Moncada and Telmo Aguilar

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