Understanding the Force on an Electron in a Changing Magnetic Field

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The discussion focuses on understanding the force acting on an electron in a time-varying magnetic field, described by the equation B = (5.00t^3 - 1.00t^2 + 0.800) T. The user is uncertain about the appropriate equations to use, initially considering the electric force equation F = qE and the relationship between electric and magnetic fields. They mention a specific equation for the electric field, E = -r/2 * dB/dt, but doubt its sufficiency for solving the problem. Additionally, the user is confused about the relevance of the radius r2 being outside the magnetic field region, which affects the forces acting on the electron. The key takeaway is that the total force on the charged particle combines both electric and magnetic components, and understanding the context of the radius is crucial for accurate calculations.
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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!
 

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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?
 
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??
 
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.
 

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