Three particles labeled a, b, and c enter a region of magnetic field that is dir

Question

Three particles labeled a, b, and c enter a region of magnetic field that is directed into the page as shown below. The particles are deflected as indicated in the diagram. What can be said about the charge of each particle? A long straight wire carries a current of I = 4 A to the right as depicted in the figure below. Consider 4 different electrons each of which are a perpendicular distance of 0.05 m from the wire. Each electron has a speed of 10^7 m/s. The direction of the electron velocities are as indicated in the diagram. Find the size and direction of the magnetic force, due to the current carrying wire, on each electron in the figure. Note the velocity of electron 4 is at an angle of 45 degree abobe the horizontal.

Explanation / Answer

1. given that the magnetic field is directed into the page
and that magnetic forceis given by F = q v x B
so from flemings left hand rule
a is +vely charged
b is neutral
c is negatively charged
2. given d = 0.05m
I = 4A
v = 10^7 m/s
now, magnitude of magnetic field at distance d from the wire , B = 2kI/d where k = 10^-7
B = 2*10^-7*4/0.05 = 0.000016 T
F = qV x B

for partticles 1 and 2, B is out of page
For force on particle 1 , v is parallel to B, so F1 = 0
For particle 2
F2 = 1.6*10^-19*10^7*0.000016 = 2560*10^-20 N, to the right
For particle 3, F3 = 1.6*10^-19*10^7*0.000016 = 2560*10^-20 N, Downwards
For particle 4, F4 = 1.6*10^-19*10^7*0.000016 = 2560*10^-20 N, 45 degree below x axis

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