Understanding the Force on an Electron in a Changing Magnetic Field

[edlin]

The Force on an Electron...??

Again, hi! I am very thankful for the help that I am being provided. I am yet again stuck in a problem.

I really do not understand it.

For the situation described in Figure P31.32, the magnetic field changes with time according to the expression B = (5.00t3 - 1.00t2 + 0.800) T, and r2 = 2R = 5.00 cm.

(I have also attached the image).

Right now, I have not really tried to solve it, because I want to understand the concept first, but I really don't get it...mostly because I am not sure what equations would be appropriate.

(1) I have thought the equation for electric force would be useful, since they do involve an electron in the problem, and it's what we want to find. Fe = qE.

By deriving B in the problem, is it correct to say that I got the E field? (Which would therefore allow me to get the Force)

(2) Then I saw in the section where this problem appeared, that they use another type of equation for the E field, which is:

E = -r/2 * dB/dt

I don't believe that using just these equations in (1) and (2) will give me the right answer though, but after that I don't know what else I am supposed to assume or do.


(3) Also, since the r2 is outside of the circle in the image, I am assuming this is important. But I don't know how to include this in the problem.


I guess that mostly it's the concept that I don't understand. I really appreciate any help that I may get. Thankyou!

 

[berkeman]

The general vector force on a charged particle in a combination E and B field is

$$F = (q E) + (q v X B)$$

Does that help?

 

[edlin]

I did see that equation though, but I'm not sure how I would get the velocity.

And does it matter that r is outside the circle??

 

[berkeman]

The velocity of the charged particle is changed by the F=ma force on it. The force on the charged particle comes from the qE + qv X B forces acting on it. And you are correct, if the B only exists insice that circle, then the qv X B force goes away outside the circle.