Yo „B. 2w 3w 4w Sw A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a non-conducting cart as shown above. The cart is placed on the inclined portion of a track and released from rest at position P, at a height y, 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 out of 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. a) Show all work (starting with equations from the equation sheet) to determine the speed of the cart when it reaches the horizontal portion of the track. b) Determine the following for the time at which the cart is at position P,, with one-third of the loop in the magnetic field. i. The magnitude of the emf induced in the conducting loop ii. The magnitude of the current induced in the conducting loop c) i. Using the axes below as a guide to draw on your own paper, sketch a graph of the magnitude of the magnetic flux D 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. i. Using the axes below as a guide to draw on your own paper, sketch a graph of the current induced in 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. Let counterclockwise current be positive and label appropriate values on the vertical axis. Counterclockwise Current 13w !4w 2w 3w 4w 5w Clockwise Current
Yo „B. 2w 3w 4w Sw A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a non-conducting cart as shown above. The cart is placed on the inclined portion of a track and released from rest at position P, at a height y, 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 out of 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. a) Show all work (starting with equations from the equation sheet) to determine the speed of the cart when it reaches the horizontal portion of the track. b) Determine the following for the time at which the cart is at position P,, with one-third of the loop in the magnetic field. i. The magnitude of the emf induced in the conducting loop ii. The magnitude of the current induced in the conducting loop c) i. Using the axes below as a guide to draw on your own paper, sketch a graph of the magnitude of the magnetic flux D 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. i. Using the axes below as a guide to draw on your own paper, sketch a graph of the current induced in 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. Let counterclockwise current be positive and label appropriate values on the vertical axis. Counterclockwise Current 13w !4w 2w 3w 4w 5w Clockwise Current
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