An electric charge in an electric field always experiences an electric force. A charge in a magnetic field, however, does not necessarily experience a magnetic force.

Stationary Charge

Just like a wire carrying zero current experiences no magnetic force, a stationary charge does not experience any magnetic force. This is because and . In the absence of other forces, this charge simply remains at rest.

__v__ parallel to *B*

Just like a current carrying conductor placed parallel to a magnetic field experiences no magnetic force, a charge moving parallel to the direction of *B* does not experience any magnetic force. This is because and . In the absence of other forces, this charge simply continues moving at velocity *v*.

__v__ perpendicular to *B*

A charge moving perpendicular to the direction of *B*, however, does experience the magnetic force . It is important you realize that *F*_{b} is always perpendicular to *v* no matter how *v* rotates and turns. If *F*_{b} is the only force acting on this charge, this charge will be traveling along a circular path![1]

For a particle of mass *m* and charge *q*, we have

To find *T*, the time taken for one complete revolution, we can divide the distance by speed:

Two interesting results:

- For the same
*v* and *B*, the radius of circular motion is directly proportional to , the mass to charge ratio. This relationship is the basis for mass spectroscopy.
- The time taken for a charged particle to complete one revolution is independent of its speed. This result is exploited in the design of particle accelerators called cyclotrons.

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**Demonstration**

CRT Magic

Magnetic Pump

**Concept Test**

2836

[1] This is not so for the electrons drifting in a current-carrying conductor because they are constrained by the metallic bonds to drift inside the wire.

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