Part 1 A beam of protons is moving in the + x direction with a speed of 13.7 km/

Question

Part 1
A beam of protons is moving in the +x direction with a speed of 13.7 km/s through a region in which the electric field is perpendicular to the magnetic field. The beam is not deflected in this region. If the magnetic field has a magnitude of 0.797 T and points in the +y direction, find the magnitude and direction of the electric field. Give the x, y, and z component of the electric field numerically.
  

Part 2
Would electrons that have the same velocity as the protons be deflected by these fields? If so, in what direction would they be deflected? (pick from below)

a) yes, they would be deflected in the +x direction
b) yes, they would be deflected in the +z direction
c) yes, they would be deflected in the +y direction
d) yes, they would be deflected in the -x direction
e) yes, they would be deflected in the -z direction
f) no, they would not be deflected by these fields
g) yes, they would be deflected in the -y direction

Explanation / Answer

Velocity of proton V = 13.7i + 0.0j + 0.0k in m/s

Magnetic field B = 0.0i + 0.797j + 0.0k in T

Let electric field be E = Exi + Eyj + Ezk

Net Force F = q(E + V X B)

V X B = 0.0i + 0.0j + 10.92k

Since the protons beam is not deflected therefore the Net force F is zero.

e(E + V X B) = 0 for proton q=e

E = - V X B charge independent equation.

E = -10.92k

A)

The electric field is in negative Z direction with magnitude |E| = 10.92 Nm

B) Since the above equation for net force becoming zero is charge independent therefore

for electron also the deflection is zero.

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