How Is Magnetic Force Calculated on an Electron in a Uniform Field?

[kiwikahuna]

Homework Statement

An electron in a vacuum is first accelerated by a voltage of 48200 V and then enters a region in which there is a uniform magnetic field of 0.183 T at right angles to the direction of the electron's motion. What is the force on the electron due to the magnetic field?

Homework Equations

F = qvBsintheta

The Attempt at a Solution

U = Vq (potential energy)
1/2 mv^2 (kinetic energy)
I set potential energy equal to kinetic energy to solve for velocity.

Vq = 1/2 mv^2 (then solve for v)
v = SQRT(2qv/m)

F = qB(SQRT(2qv/m))sintheta
Plugging in the numbers, I get
F = (1.6e-19) (0.183T) (SQRT(2(1.6e-19)*48200V/9.11e-31))* sin (90)
F = 3.82 e -12

Is this the right way to do this problem? Thanks in advance for looking it over for me.

 

[G01]

You seem to be correct as long as the electron starts off at a velocity of 0, which I'm assuming it does since the problem does not state otherwise. I also get the same answer that you do. Nice job!

 

[m2003]

Your approach is correct, and your final answer of 3.82e-12 is in the correct unit of Newtons (N). However, there are a few minor errors in your calculation. First, the charge of an electron is negative, so you should use -1.6e-19 instead of 1.6e-19. Second, when plugging in the values for q and B, make sure to use the same unit for both (either Coulombs for q or Amperes for B). Finally, the sin(90) term is unnecessary since the angle between the velocity and the magnetic field is already accounted for in the equation. Overall, your approach is correct and you have the right idea for solving this problem. Keep up the good work!