Question

An electric field E exerts a force F on an ion of charge q. At right angles to the electric field is a magnetic field B. a. Write an equation for the speed of the ion if the electric and magnetic forces are equal and opposite. b. Calculate the speed if the charge of the ion is 1.6E-19 C, the electric field is 6.0E6 N/C, and the magnetic field is 0.83 T. c. If the charge were twice as great, what strength of the magnetic field would result in a straight line path? d. If the ion had instead double the mass, what strength of the magnetic field would result in a straight line path?

Answer 1

a)
From the Lorentz force equation
  

Thus the speed does not depend upon the charge. It depends upon the electric field E and the magnetic field B.

b)
  Given, E = 6 E6 N/C, and B = 0.83 T, we get

c)
Straight line path implies the cancellation of the electric and magnetic forces. And this further implies

As this is independent of the charge, so, even if the charge is doubled, the magnetic field is the same as before for the above equation to hold.
d)
Again the above expression is independent of the mass. So, even if the mass is doubled, the magnetic field is same as before for the above equation to hold.