Agroup of particles is traveling in a magnetic field of unknown magnitude and direction. you observe that a proton moving at 1.20 km/s in the +x-direction experiences a force of 2.10×10−16 n in the +y-direction, and an electron moving at 4.20 km/s in the −z-direction experiences a force of 8.40×10−16 n in the +y-direction. part a what is the magnitude of the magnetic field?

To find the magnitude of the magnetic field, we can use either the proton or the electron.

The magnetic force experienced by a charged particle moving in a magnetic field is:

where
q is the charge
v is the velocity of the particle
B is the magnitude of the magnetic field
is the angle between the direction of v and B.

Let's take the proton. The particle is moving in the x-direction, while the force is in the y-direction: for the right-hand rule, this means that the magnetic field B is in the z-direction, so v and B are perpendicular and , so  and we can ignore it in the formula.

Therefore, we have:

or

and since we know the force intensity, the velocity of the proton v and its charge (), we can find the magnitude of B: