Answer to Question #267275 in Electric Circuits for zuzu

Question

a) A beam of protons moves at 3.0 x 10⁵ m/s through a uniform magnetic field with magnitude 2.0 T and whose direction makes an angle of 32o with respect to the proton's velocity. Find the velocity and magnitude of the force on the proton.

b) What is the maximum force on an aluminum rod with a 0.2μC charge that is crossed between the poles of a 2.5T permanent magnet at a speed of 6m/s? In what direction is the force? 

Answer 1

a)

force on the proton:

$\vec{F_B}=q(\vec{v}\times\vec{B})$

$F=|q|vBsin\theta=1.6\cdot10^{-19}\cdot3\cdot10^5\cdot2sin32\degree=5.09\cdot10^{-14}$ N

direction is upward

b)

maximum force:

$F=|q|vBsin90\degree=0.2\cdot10^{-6}\cdot6\cdot2.5=3\cdot10^{-6}$ N

direction is perpendicular to line connecting poles and proton speed direction