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Magnetic Force on Moving Charge
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?
Facts
- 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 $\vec{v} = 10 \text{ m/s } \hat{y}$.
Lacking
- $\vec{F}_B$
Approximations & Assumptions
- The magnetic force on the charge contains no unknown contributions.
Representations
- We represent the magnetic force on a moving charge as
$$\vec{F}= q \vec{v} \times \vec{B}$$
- We represent the two situations below.
Solution
The trickiest part of finding magnetic force is the cross-product.