Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
Magnetic Torques and Amp's Law
- A magnetic field exerts a force on a straight wire carrying
current; it exerts a torque on a loop of wire carrying
current.
- Torque causes an object to spin around a fixed axis.
- Each loop of current has a direction associated with it:
its normal vector is perpendicular to the loop,
in the direction given by the right thumb when the right fingers
curl in the direction of the current.
- A magnetic field exerts a torque which tries to align the
normal vector of a loop of current with the magnetic field.
- The size of the torque on a loop of current is
torque = (# turns) * (current) * (loop area) * (mag field) * sin(theta)
where theta is the angle between the magnetic field and the loop's
normal vector.
- A loop carrying direct current will not keep spinning in a
constant magnetic field; it will instead just wobble back and forth.
DC motors must use a split-ring commutator to permit them to
spin fully around.
- It is possible to create a magnetic field by running a current
through a wire -- showing the close relationship between
electricity and magnetism.
- Ampere's Law permits one to calculate the strength of a magnetic
field created by current in several simple situations.
- The strength of a magnetic field around a long, straight wire is
mu * current
mag field = -------------------
2 * pi * distance
where mu is the magnetic permeability of free space:
mu = 4 * pi * 10^(-7) T*m/A
= 1.257 x 10^(-6) T*m/A
- The strength of a magnetic field at the center of a loop of wire is
N * mu * current
mag field = -----------------
2 * radius
where N is the number of turns of wire in the loop.
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Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.