Slide Wire on a V-Shaped Track: Calculating EMF, Current & Area

AI Thread Summary
The discussion focuses on calculating the electromotive force (EMF) and current for a slide wire moving along a V-shaped track in a constant magnetic field. The principle for calculating the magnitude of the motional EMF is based on Faraday's law of electromagnetic induction. The direction of the current is determined by the right-hand rule, which relates the direction of motion and the magnetic field. The area enclosed by the slide wire is expressed in terms of the position x and the angle q of the slanted line. The induced EMF is a function of both the position x(t) and the velocity v(t), which can be derived algebraically.
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A slide wire (resistance R) travels without friction along the track shown below. It starts from position x0 (non-zero) and velocity v0 , to the right as shown. Assume that the v shaped rails meet at an angle of q. Use the coordinate system shown.



The magnitude of the external magnetic field is constant. The direction of the external magnetic field is also constant (into the page).
a.) State the principle that describes how to calculate the magnitude of the motional electromotive force (this can be an equation).

b.) State the principle that describes how to compute the direction of the current associated with the electromotive force. (words)

c.) Write the equation of the area enclosed in terms of x only. (Hint: What is the equation of the slanted line? Write the slope in terms of q.)

d.) Find the induced electromotive force. This will be a function of both x(t) and v(t).

e.) What is v(t)? (Algebraic equation for v(t).)
 

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