Question

5) PO WIX X X X X X X X X X P₂0 4 20 30 40 Sw A rectangular conducting loop of width w, height , and resistance R is mounted vertically on a noncon- ducting cart as shown above. The cart is placed on the inclined portion of a track and released from restat position at a height yo 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. (a) 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 B, 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) On the following dingram of the conducting loop, indicate the direction of the current when it is at position B. (d) 1. Using the axes below, sketch a graph of the magnitude of the magnetic flux 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. ii. Using the axes below, sketch a graph of the current induced in the loop as a function of the horizontal distance x traveled by the cart, letting = 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 Clockwise Current

Answer 1

cas speed aut ground By conservation of enersy. [v=Vagyo ph gy = 1202 asis= houdt » Loop in side the field. mu le=-Bvh =-B/2g6h i i - BVA 1239 h O since magnetic field want to move ed in clockwise, fonemas Corrent meres Anticlock wise, this Ak to Rena's law it resist that Change. so, Current porodne in loop [Clockwise Area increasing for loop, during a for look, during oyw so flux increase. waw Constand 3w-uw diren decreating - de Antil clock helicate sign so -ve 4W X 2w Clock