Faraday's Law and electron force

[Ithryndil]

Homework Statement

For the situation described in Figure P31.32, the magnetic field changes with time according to the expression B = (8.00t^3 - 4.00t^2 + 0.800) T, and r2 = 2R = 5.00 cm.

Figure P31.32
(a) Calculate the magnitude and direction of the force exerted on an electron located at point P2 when t = 2.00 s.

Homework Equations

E = -0.5r(dB/dt)
F = qE + (qv X B)

The Attempt at a Solution

E = -0.5r(dB/dt)
F = qE + (qv X B)

Alright, the force equation should simplify to just F = qE because B is zero outside the circle.

When I plug in and get:
F = 0.5qr (24t^2-8t) and plug in for the values:
q = 1.602 x 10^(-19)
r = 0.05m
t = 2

I get: 3.204 x 10^(-19) which is wrong...

What am I doing wrong here?

 

[alphysicist]

Hi Ithryndil,

Homework Statement

For the situation described in Figure P31.32, the magnetic field changes with time according to the expression B = (8.00t^3 - 4.00t^2 + 0.800) T, and r2 = 2R = 5.00 cm.

Figure P31.32
(a) Calculate the magnitude and direction of the force exerted on an electron located at point P2 when t = 2.00 s.

Homework Equations

E = -0.5r(dB/dt)

I believe this is where your error is; this equation is not correct. How did you get it, and do you see what it needs to be?

 

[Ithryndil]

The equation is right out of my book.

 

[alphysicist]

The equation is right out of my book.

My guess is that in your book it is part of an example problem; in your diagram for example that equation would apply to the point P₁, but not to point P₂.

You need to derive an equation that applies to point P₂, starting with Faraday's law.

 

[Ithryndil]

Alright, yeah looks the equation applies to inside the circle, not to the outside...alright, well it's late, I will work on that derivation tomorrow after some sleep. Thanks for the insight.

 

[Ithryndil]

Thank you. I got it. The expression of E I needed is:

E = [R^2(24.0t^2 - 8.00t)]/(2r) where R is the radius of the circle and r is the radius of the electron's orbit.