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

Question

A group of particles is travelling 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 2.10×1016 N in the +y-direction, and an electron moving at 4.50 km/s in the z-direction experiences a force of 8.30×1016 N in the +y-direction.

What is the magnitude of the magnetic field?

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

What is the magnitude of the magnetic force on an electron moving in the y-direction at 3.20 km/s?

What is the direction of this the magnetic force? (in the xz-plane)

Explanation / Answer

a) Let B is the magnitude of magnetic field.

magnetic force on proton,

F = q*vx*Bz*sin(90)

==> Bz = F/(q*v)

= 2.1*10^-16/(1.6*10^-19*1.2*10^3)

= 1.094 T

magnetic force on electron,

F = -q*vz*Bx*sin(90)

==> Bx = F/(q*v)

= 8.3*10^-16/(1.6*10^-19*4.5*10^3)

= 1.15 T

B = sqrt(Bx^2 + Bz^2)

= sqrt(1.094^2 + 1.15^2)

= 1.59 T

b) direction of B is , theta = tan^-1(Bz/Bx)

= tan^-1(1.094/1.15)

= 43.6 degreees with +x axis

c) F = q*v*B*sin(90)

= 1.6*10^-19*3.2*10^3*1.59*sin(90)

= 8.14*10^-16 N

d) direction, theta = 90 - 43.6

= 46.4 with +x axis toward -y axis

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