Force on Electric Charges Moving in Electric and Magnetic Fields

What Is the Force Due to a Magnetic Field?

Magnetic fields can exert a force on an electric charge only if it moves, just as a moving charge produces a magnetic field. This force increases with both an increase in charge and magnetic field strength. Moreover, the force is greater when charges have higher velocities.

The magnetic force, however, always acts perpendicular to the velocity. Thus, this force can never produce work on the charge and cannot impart any kinetic energy. The magnetic force is given by:

Where q is the charge, v is the velocity, and B is the magnetic field.

Notice that the cross product implies that the force always acts perpendicular to the velocity and magnetic field. Thus, it always acts out of the plane and does not contribute to any work on the charge. It can merely change the direction of the velocity but cannot change its magnitude. The direction of the force can be easily determined using Fleming’s Right-hand Rule.

What Is the Force Due to Electric Field?

The force due to the electric field on a charge is built into its definition. It always acts either parallel or anti-parallel to the electric field and is independent of the velocity of the charge. This means it can do work and impart energy to the charge.

\(\begin{array}{l}\overrightarrow{F_e}  =  q ~\overrightarrow{E}\end{array} \)

What Is Lorentz Force?

When a charge travels through both an electric and magnetic field, the net force on the charge is called the Lorentz force. It is simply the sum of the magnetic and electric forces:

\(\begin{array}{l}\overrightarrow{F} = \overrightarrow{F_e}~+~\overrightarrow{F_m}\end{array} \)

\(\begin{array}{l}\overrightarrow{F} = q~\overrightarrow{E}~+~q~\overrightarrow{v}~×~\overrightarrow{B}\end{array} \)

\(\begin{array}{l}\overrightarrow{F} = q~\overrightarrow{E}~+~\overrightarrow{v}~×~\overrightarrow{B}\end{array} \)

Combinations of electric and magnetic fields are used in particle accelerators, cyclotrons and synchrotrons. The magnetic field can keep the charges moving in a circle, while the electric field accelerates the charges and imparts their energy.

Watch the Video and Learn about Force on a Moving Charge in Magnetic Field

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Frequently Asked Questions – FAQs

Q1

What is the force on a moving charge in a magnetic field?

The Lorentz force is the net force on a charge as it travels through an electric and magnetic field. It is essentially the sum of magnetic and electric forces.

Q2

What is a magnetic field?

A magnetic field is a field that describes the magnetic effect on moving charges, magnetic materials and electric currents.

Q3

Explain the force due to a magnetic field.

Magnetic fields can exert a force on an electric charge only if it is moving, just as a moving charge generates a magnetic field. This force increases with both an increase in charge and magnetic field strength. Infarct, the force is greater when charges have higher velocities.

Q4

Explain the force due to an electric field.

The force due to the electric field on a charge always acts either parallel or antiparallel to the electric field and is independent of the charge’s velocity. This means it can do work and give energy to the charge.

Q5

What is meant by the Lorenz force?

When a charge moves through an electric and magnetic field, the net force on the charge is known as the Lorentz force. It is basically the sum of the magnetic and electric forces.

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