MAG - Forces on Moving Charges Due to Magnetic Fields

Forces on Moving Charges Due to Magnetic Fields

Introduction

We've seen that a current-carrying wire experiences a force when placed in a magnetic field. Since current is just the flow of charged particles, it stands to reason that individual charged particles would also experience a force when moving through a magnetic field. While it took some time, it was finally shown that charged particles moving through a magnetic field do experience a force. This knowledge was put to practical use, much to the pleasure of people who enjoyed watching television (this connection will be covered in the discussion below).

From a mathematical standpoint we know that current is given by , where q is the charge.

The length l of the wire can be given as the velocity of a charge moving through it times the time.

If we substitute these values into the force equation:

This is the equation for the magnitude of the force acting on a charged particle moving through a magnetic field.

The direction of the force on a positively charged particle is determined by right hand rule #2. The only difference being that your thumb now points in the direction of the charge's motion rather than in the direction of the current in the wire.

Note: The right hand rule only gives the direction of the force on a positively charged particle. The direction of the force on a negatively charged particle will be in the opposite direction.

Motion of a Charged Particle in a Magnetic Field

Motion of a Charged Particle in a Magnetic Field Practice 

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