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 2.06×1016 N in the +y-direction, and an electron moving at 4.20 km/s in the z-direction experiences a force of 8.40×1016 N in the +y-direction.

Part A

What is the magnitude of the magnetic field?

Part B

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

Part C

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

Part D

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

Explanation / Answer

A) Fb = q*(v x B)

(2.06*10^-16)j^ = (1.6*10^-19)*[(1.5*10^3)i^ x B]   => B = (0.86T) -k^

And

(8.40*10^-16)j^ = (-1.6*10^-19)*[(4.2*10^3)-z^ x B]    => B = (1.25 T) i^

Thus B = (1.25 T) i^ + (0.86T) -k^

B= sqrt(1.25^2 + 0.86^2) = 1.52 T

B) = sin^-1(0.86/1.25) = 43.47 deg directed from +x to –z axis.

C) Fb = q*(v x B)

Fb = (-1.6*10^-19)*[(3.7*10^3)-j^* (1.25 T) i^ + (0.86T) -k^ ] = [(1.6*10^-19*3.7*10^3*1.25)*-(-j x i) + (1.6*10^-19*3.7*10^3*0.86)*-(-j x -k)] = (7.4*10^-16) -k^   + (5.09*10^-16) -i^

B = sqrt[(7.4*10^-16) ^2 + (5.09*10^-16)^2] = 9.0*10^-16 N

D) = sin^-1[(5.09*10^-16)/(7.4*10^-16)] = 43.46 deg directed from -x to -z axis.

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