Question

A group of particles is traveling in a magnetic field of unknown magnitude and direction. You observe that a proton moving at 1.30 km/s in the +x-direction experiences a force of 2.10×10−16 N in the +y-direction, and an electron moving at 4.50 km/s in the −z-direction experiences a force of 8.60×10−16 N in the +y-direction. What is the magnitude of the magnetic field?

b-What is the direction of the magnetic field? (in the xz-plane)

Answer 1

The z component of the magnetic field is
-2.x10^(-16)N/(1.602x10(-19)C x 1.30 x 10^3 m/s) = 0.9603 T

The x component of the magnetic field is
8.6 x 10^(-16)N / (1.602x10^(-19)C x 4.5 x 10^3 m/s) = 1.192 T,
but we can't know whether this is positive or negative,
because you didn't say whether the electron is deflected
in the +y direction or the -y direction.
If I assume that the force on the electron also acts in the +y direction,
then the x component of the magnetic field is also positive,
since (-)(-k) x (i) = +j.
I conclude that the magnetic field has magnitude
sqrt(1.192^2 + 0.9603^2) T = 1.53 T
and its direction is in the x-z plane at
arctan (0.9603/1.192) = 38.85 degrees away from the + x-axis
and 51.15 degrees away from the + z-axis.