Acceleration of an electron in both a magnetic and an electric field

[lynkyra]

Homework Statement

Let E = 4 N/C in the x direction and B = 4 T in the -z direction. Let an electron move in the y-direction
with speed 1m/s. What is the magnitude of the acceleration of the electron in m/s2?

Homework Equations

F_m=qv X B
F_{electric field}=qE
F=ma

The Attempt at a Solution

I plugged in values and found F_m to equal -6.408X10^-19N and found F_{electric field} to also equal -6.408X10^-19N. I'm not sure my sign is right on the first one because I was confused about the flow of the electron versus the flow of the current...

F=ma, and since I know the mass of an electron and I'm trying to find the acceleration, I think that I should add my two forces to get a total force, which equals ma. I did this and got a=4.508X10^-7. I think this is wrong, though, because I think an acceleration would be larger than that.

 

[gneill]

Yes, check your signs. The directions of the forces are key. When in doubt, set up the vectors (they're very simple in this case) and carry out the vector math to find the resultant force. You may find that the net acceleration is smaller than you think

 

[lynkyra]

I would check my signs, but I don't know what they should be. I'm not good with vectors and I don't fully understand what a cross product is. Also, my instructor implied that the answer to this question was only X10^-(1,2, or 3).

 

[gneill]

A negatively charged electron is accelerated "upstream" in an electric field. Remember that when you draw a diagram showing an electric field, the field arrows are shown emanating out of positive charges and into negative charges (think of the electric field between capacitor plates). A negative charge is attracted by a positive charge. So the electron heads "against" the arrow directions. On the other hand a positive charge does the opposite and accelerates in the same direction as the field arrows.

For magnetic fields you should learn to use the right-hand rule to find the direction of the force. The right-hand rule tells you the direction that results from performing a cross product of vectors (in this case velocity crossed with magnetic field). Comes in very handy (pun!) in many situations where cross products come up.

 

[Nickie]

Your calculations are correct. The acceleration of the electron in this scenario is indeed 4.508 x 10^-7 m/s^2. This may seem small, but it is actually quite significant for an electron. Keep in mind that the mass of an electron is very small, so even a small acceleration can have a significant effect on its motion. Also, the negative sign in your calculations indicates that the acceleration is in the opposite direction of the velocity, which is to be expected since the forces from the magnetic and electric fields are acting against the motion of the electron in the y-direction.