A group of particles is traveling in a magnetic field of unknown magnitude and d

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 2.06 times 10^-16 N in the +-y-direction, and an electron moving at 4.40 km/s in the -z-direction experiences a force of 8.20 times 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) theta = What is the magnitude of the magnetic force on an electron moving in the - y-direction at 3.40 km/s?

Explanation / Answer

A)

force on proton

F = q*v*Bz

2.06*10^-16 = 1.6*10^-19*1.3*10^3*B

Bz = -0.99 T

Force on electron is F = q*v*Bx

Bx = F/(q*v) = (8.2*10^-16)/(1.6*10^-19*4.4*1000) = 1.164 T

B = 1.164 i - 0.99 k

magnitude is B = sqrt(1.164^2+0.99^2) = 1.528 T

B) theta = tan^(-1)(Bx/Bz) = tan^(-1)(1.164/0.99) = 49.6 degrees

C) F = q*v*B = 1.6*10^-19*3.4*1000*1.528 = 8.312*10^-16 N

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