Magnetic Force

The magnetic field B is defined from the Lorentz
Force Law, and specifically from the magnetic force on a moving
charge:

The implications of this expression include:

1. The force is perpendicular to both the velocity v of the charge q
and the magnetic field B.

2. The magnitude of the force is F = qvB sin
where
is the angle < 180 degrees between the velocity and the magnetic field.
This implies that the magnetic force on a stationary charge or a charge
moving parallel to the magnetic field is zero.

3. The direction of the force is given by the right
hand rule. The force relationship above is in the form of a vector
product.

From the force relationship above it can be deduced that the units of
magnetic field are Newton seconds /(Coulomb meter) or Newtons per Ampere
meter. This unit is named the Tesla. It is a large unit, and the smaller
unit Gauss is used for small fields like the Earth's magnetic field. A
Tesla is 10,000 Gauss. The Earth's magnetic field is on the order of half
a Gauss.

Magnetic
interactions with charge

Magnetic
force applications

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Electromagnetic
force

Magnetic
field concepts

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Lorentz Force Law

Both the electric
field and magnetic
field can be defined from the Lorentz force law:

The electric force is straightforward, being in the direction of the
electric field if the charge q is positive, but the direction of the
magnetic part of the force is given by the right
hand rule.

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Electromagnetic
force

Magnetic
force

Magnetic
field concepts

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Right Hand Rule

The right hand rule is a useful mnemonic for visualizing the direction
of a magnetic
force as given by the Lorentz
force law. The diagrams above are two of the forms used to visualize
the force on a moving positive charge. The force is in the opposite
direction for a negative charge moving in the direction shown. One fact to
keep in mind is that the magnetic force is perpendicular to both the
magnetic field and the charge velocity, but that leaves two possibilities.
The right hand rule just helps you pin down which of the two directions
applies.

For applications to current-carrying wires, the conventional
electric current direction can be substituted for the charge velocity
v in the above digram.

Magnetic
force as a vector product

Magnetic
force on a moving charge

Index

Magnetic
force

Magnetic
field concepts

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Electricity and Magnetism

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