Problem 26-36a: A beam of protons is moving in the + x direction with a speed of

Question

Problem 26-36a:
A beam of protons is moving in the +x direction with a speed of 10.4 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 0.842 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.
  

Problem 26-36b:

Would electrons that have the same velocity as the protons be deflected by these fields? If so, in what direction would they be deflected?

yes, they would be deflected in the -x direction
yes, they would be deflected in the -y direction
yes, they would be deflected in the +z direction
no, they would not be deflected by these fields
yes, they would be deflected in the -z direction
yes, they would be deflected in the +x direction
yes, they would be deflected in the +y direction

Explanation / Answer

Prob 26-36a) Magnetic force on each proton, Fm = qp(v x B) = (qpvB) k^

Since the magnetic force is in the positive z-direction, electric force needs to be in negative z-direction for the net force on the electron to be zero.

Electric force, Fe = -(qpE) k^

So, qpE = qpvB

=> E = vB = (10.4 * 103) * 0.842 = 8.76 N/C

SInce proton is a positive charge, the direction of electric field is towards the negative z-axis.

Prob 26-36b) The electrons will not be deflected since the required electric field for no-deflection condition does not depend on the charge as we see above in the previous problem.

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