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Homework Statement
The figure attached shows a rod of length L = 10 cm that is forced to move a a constant speed of v = 5.00 m/sec along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has a resistance of 0.4 [tex]\Omega[/tex] and the rest of the loop has negligible resistance. A current of 100 A through the long straight wire at a distance a = 10.0 mm from the loop sets up a nonuniform magnetic field through the loop.
Find the emf and current induced in the loop.
Note: sorry about the shotty diagram... paint is a cruel mistress... the x's are the B field going into the page and the *'s are coming out of the page.... the point is that the field is NOT uniform.
Homework Equations
1. [tex] \Phi_B = \int{\vec{B} \bullet d\vec{A}} [/tex]
2. [tex] \epsilon = B l v[/tex]
3. [tex] B = \frac{\mu_0}{2\pi} \frac{I}{r} [/tex]
4. [tex] \epsilon = \frac{d \Phi_B}{dt}[/tex]
5. [tex] I = \frac{\epsilon}{R}[/tex]
The Attempt at a Solution
I feel like finding the current is pretty simple once I've managed to calculate the emf by using eqn # 5.
The emf is where I am really struggling. I know that I can calculate the flux (and be able to deduct the emf) using eqn #3 as a function for B. But that requires I know the area of the loop and I'm pretty sure I have insufficient information for that.... Equation 2 gives me the B field at a point (again, subing eqn 3 for B) but that doesn't really help me...
I've been looking through my book and the internet for hours.. but I am missing something.. A push in the right direction would be much appreciated....
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