A particle with a charge of 31 uC moves with a speed of 74 m/s in the positive x

Question

A particle with a charge of 31 uC moves with a speed of 74 m/s in the positive x direction. The magnetic field in this region of space has a component of 0.40 T in the positive y direction, and a component of 0.83 T in the positive z direction.

Part A:

What is the magnitude of the magnetic force on the particle?

F = ???   mN

Part B:

What is the direction of the magnetic force on the particle? (Find the angle measured from the positive z-axis toward the negative y-axis in the yz-plane.)

? =    ??? degrees  

Explanation / Answer

F = q*[|v||B| sin(theta)]

F_z = 31*(10^-6)*74*0.4*sin 90 = 9.176*10^-4 N (positive z axis)

F_y = 31*(10^-6)*74*0.83*sin 90 = 1.904*10^-3 N (negative y axis)

|F| = 2.11*10^-3 N

theta = arctan ( 1.904*10^-3/9.176*10^-4 ) = 64.27 degree

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