Suppose you have a moving charge ($q=1.5 \text{ mC}$) in a magnetic field ($\vec{B} = 0.4 \text{ mT } \hat{y}$). The charge has a speed of $10 \text{ m/s}$. What is the magnetic force on the charge if its motion is in the $+x$-direction? The $+y$-direction?

• The charge is $q=1.5 \text{ mC}$.
• There is an external magnetic field $\vec{B} = 0.4 \text{ mT } \hat{y}$.
• The velocity of the charge is $\vec{v} = 10 \text{ m/s } \hat{x}$ or $\vec{v} = 10 \text{ m/s } \hat{y}$.

• $\vec{F}_B$

• The magnetic force on the charge contains no unknown contributions.

• We represent the magnetic force on a moving charge as

$$\vec{F}= q \vec{v} \times \vec{B}$$

• We represent the two situations below.

The trickiest part of finding magnetic force is the cross-product.