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Unformatted text preview: Physics 21 Fall, 2009 Solution to HW-16 28.48 The current in the windings of a toroidal solenoid is 2.400 A. There are N = 500 turns and the mean radius is r = 25 . 00 cm. The toroidal solenoid is filled with a magnetic material. The magnetic field inside the windings is found to be 1.940 T. (a) Calculate the relative permeability. (b) Calculate the magnetic susceptibility of the material that fills the toroid. (a) The magnetic field inside a tightly wound toroidal solenoid is B = K m nI = K m NI 2 r , where n is the number of turns per unit length and N is the total number of turns. Solving the last equation for K m , we get K m = 2 rB NI = 2 . 25 1 . 94 (4 10- 7 ) 500 2 . 4 = 2021 . (b) The magnetic susceptibility is m = K m 1 thus the answer is 2020. Faradays Law Consider a rectangular loop of wire with sides x and y placed in a region where a uniform magnetic field B exists (see the diagram). The resistance of the loop is R . Initially, the field is perpendicular to the plane of the loop and is directed out of the page. The loop can rotate about either the vertical or horizontal axis, passing through the midpoints of the opposite sides. (a) (multiple choice) Which changes would induce an electro- motive force (emf) in the loop? (b) Find the ux through the loop. (c) If the magnetic field steadily decreases from B to zero during a time interval t , what is the magnitude E of the induced emf? (d) If the magnetic field steadily decreases from B to zero during a time interval t , what is the mag- nitude I of the induced current? (e) If the magnetic field steadily decreases from B to zero during a time interval t , what is the direction of the induced current? (f) (multiple choice) Which changes would result in a clockwise emf in the loop?...
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