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 1.60 km/s in the +x-direction experiences a force of 2.06×1016 N in the +y-direction, and an electron moving at 4.60 km/s in the z-direction experiences a force of 8.40×1016 N in the +y-direction.

A.) What is the magnitude of the magnetic field?

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

C.) What is the magnitude of the magnetic force on an electron moving in the y-direction at 3.70 km/s ?

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

Explanation / Answer

part a )

Force on proton in -z direction

Bz = -Fp/q*vp = 2.06 x 10^-16 / 1.6x10^-19*1600 m/s = -0.805 Tk

force on electron in + x direction

Bx = Fe/q*ve = 8.40 x 10^-16 / 1.6x10^-19 x 4600 = 1.14 T i

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

B = 1.4 T

part b )

theta = tan^-1(Bz/Bx) = 35.23 degree

part c )

B = Bx i + Bz k

F = q( v x B)

F = q * 3700 ( - 1.14 k - 0.805 i ]

F = -6.7488 x 10^-16 k - 4.7656 x 10^-16

|F| = 8.26 x 10^-16 N

part D )

theta = tan^-1(Fz/Fx) = 54.77 degree

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