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- Homework Statement
- A circuit with resistance R, a moving bar of lenght l and mass m has initial velocity along the x-axis = -v and at t=0 the bar is in position x=2l. The circuit lays in a region with depending on the x-coordinate. Find the current flowing in the circuit.

- Relevant Equations
- Faraday's law

The amplitude of ##\vec{B}## is given by:

$$B(x) = B_{0} - B_{0} \frac{x}{2l}$$ for ##0 \leq 0 \leq 2l##

This was my attempts at finding the flux of B:

$$\Phi(B) = (B_{0} - B_{0} \frac{x}{2l})(2l-x(t))l = B_{0}2l^2-2B_{0}x(t)l+ B_{0}\frac{x(t)^2}{2}$$

and the current: $$ i = -\frac{d \Phi(B)}{dt} \frac{1}{R} = -\frac{B_{0} v(t) (2l -x(t))}{R}$$

Is this approach correct?

$$B(x) = B_{0} - B_{0} \frac{x}{2l}$$ for ##0 \leq 0 \leq 2l##

This was my attempts at finding the flux of B:

$$\Phi(B) = (B_{0} - B_{0} \frac{x}{2l})(2l-x(t))l = B_{0}2l^2-2B_{0}x(t)l+ B_{0}\frac{x(t)^2}{2}$$

and the current: $$ i = -\frac{d \Phi(B)}{dt} \frac{1}{R} = -\frac{B_{0} v(t) (2l -x(t))}{R}$$

Is this approach correct?