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 1.50 km/s in the + x-direction experiences a force of 2.10 times 10^-16 N in the +y-direction, and an electron moving at 4.60 km/s in the -z-direction experiences a force of 8.50 times 10^-16 N in the + y-direction What is the magnitude of the magnetic force on an electron moving in the - y-direction at 3.60 km/s? What is the direction of this the magnetic force? (in the xz-plane)

Explanation / Answer

B = Bx i + By j + Bz k

For proton:

v = 1500 m/s i

F = q (v x B)

F = (q v By) k + (q v Bz)(-j )

force F is along j so By = 0

Bz = - F / q v = - (2.10 x 10^-16) / (1.602 x 10^-19 x 1500)

Bz = - 0.874 T

for electron:

v = 4600 m/s (-k )

F = q (v x B)

F = - (q v Bx) j   

Bx = (8.50 x 10^-16) / (1.602 x 10^-19 x 4600) = 1.15 T

B = 1.15i - 0.874k

F = (-1.602 x 10^-19) [ -3600j X (1.15i - 0.874k )]

= - 6.63 x 10^-16k - 5.04 x 10^-16 i

(C) magnitude = sqrt(6.63^2 + 5.04^2) x 10^-16

= 8.33 x 10^-16 N

(D) theta = tan^-1( 6.63 / 5.04) = 52.8 deg

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