A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a nonconducting cart as shown in the drawing. The cart is placed on the inclined portion of a track and released from rest at position P1 at a height of y0 above the horizontal portion of the track. It rolls with negligible friction down the incline and through a uniform magnetic field B in the region above the horizontal portion of the track. The conducting loop is in the plane of the page, and the magnetic field is directed into the page. The loop passes completely through the field with a negligible change in speed. Express your answers in terms of the given quantities and fundamental constants. 1. Find the speed of the cart when it reaches the horizontal portion of the track. 2. Determine the magnitude of the emf and current induced in the conducting loop for the time at which the cart is at position P2 with one-third of the loop in the magnetic field. 3. Using the axes, sketch a graph of the magnitude of the magnetic flux f through the loop as a function of the horizontal distance x traveled by the cart, letting x = 0 be the position at which the front edge of the loop just enters the field. Label appropriate values on the vertical axis.
A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a nonconducting cart as shown in the drawing. The cart is placed on the inclined portion of a track and released from rest at position P1 at a height of y0 above the horizontal portion of the track. It rolls with negligible friction down the incline and through a uniform magnetic field B in the region above the horizontal portion of the track. The conducting loop is in the plane of the page, and the magnetic field is directed into the page. The loop passes completely through the field with a negligible change in speed. Express your answers in terms of the given quantities and fundamental constants.
1. Find the speed of the cart when it reaches the horizontal portion of the track.
2. Determine the magnitude of the emf and current induced in the conducting loop for the time at which the cart is at position P2 with one-third of the loop in the magnetic field.
3. Using the axes, sketch a graph of the magnitude of the magnetic flux f through the loop as a function of the horizontal distance x traveled by the cart, letting x = 0 be the position at which the front edge of the loop just enters the field. Label appropriate values on the vertical axis.
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