Magnetic force

Definition

Magnetic force is the force exerted by a magnetic field on a moving electric charge or a current-carrying conductor. It is perpendicular to both the velocity of the charge and the magnetic field.

5 Must Know Facts For Your Next Test

1. The magnitude of the magnetic force on a moving charge is given by $F = qvB\sin(\theta)$, where $q$ is the charge, $v$ is its velocity, $B$ is the magnetic field strength, and $\theta$ is the angle between $v$ and $B$.
2. The direction of the magnetic force is determined using the right-hand rule for positive charges and left-hand rule for negative charges.
3. For a current-carrying conductor in a magnetic field, the force per unit length can be calculated using $F = ILB\sin(\theta)$, where $I$ is current, $L$ is length of conductor in field, and other symbols have their usual meanings.
4. Magnetic forces do no work on charges since they act perpendicular to displacement; thus they only change the direction of motion.
5. In uniform circular motion caused by a magnetic field, centripetal force equals magnetic force: $qvB = \frac{mv^2}{r}$. This relation helps derive radius of path: $r = \frac{mv}{qB}$.

Review Questions

• What factors determine the magnitude of the magnetic force experienced by a moving charge?
• How does one use the right-hand rule to find the direction of magnetic force?
• Why can’t magnetic forces do work on charged particles?

Related terms

Magnetic Field:

A region around a magnetic material or a moving electric charge within which the force of magnetism acts.

Lorentz Force:

The combined electric and magnetic force on a point charge due to electromagnetic fields, given by $F = q(E + v \times B)$.

Right-Hand Rule:

A mnemonic for understanding orientation conventions for vector fields such as those in electromagnetism; particularly used to find direction of magnetic forces.