iPad 6:42 PM 41% . EXAMPLE 20.2 Faraday and Lenz to the Rescue GOAL Calculate an
ID: 2037734 • Letter: I
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iPad 6:42 PM 41% . EXAMPLE 20.2 Faraday and Lenz to the Rescue GOAL Calculate an induced emf and current with Faraday's law and apply Lenz's law when the magnetic field changes with time. PROBLEM A coil with 25 turns of wire is wrapped on a frame with a square cross section 1.80 cm on a side. Each turn has the same area, equal to that of the frame, and the total resistance of the coil is 0.350 2. An applied uniform magnetic field is perpendicular to the plane of the coil, as in the figure. (a) If the field changes uniformly from 0.00 T to 0.500 T in 0.800 s, what is the induced emf in the coil while the field is changing? Find (b) the magnitude and (c) current in the coil while the field is changing the direction of the induced STRATEGY Part (a) requires substituting into Faraday's law, ? NasB. The necessary information is At given, except for ???, the change in the magnetic flux during the elapsed time, using the normal direction to coincide with the positive z-axis, compute the initial and final magnetic fluxes with ?8 BIA BA cos , find the difference, and assemble all terms in Faraday's law. The current can then be found with Ohm's law, and its direction with Lenz's law SOLUTION (a) Find the induced emf in the coil. To compute the flux, the area of the coil is needed. A L2(o.0180 m)2 3.24 x 104 m2 ?6/ . (0.500 T)(3.24x 10-4 m2)cos(0) The magnetic flux ?, through the coil at t 0 is zero because B 0 Calculate the flux at t 0.800 s. BA cos 1.62 x 104 Wb Compute the change in the magnetic flux through the cross section of theExplanation / Answer
(A) e = d(flux)/dt
e = N A dB/dt
e = (22)(0.0211^2) (0.403 - 0.222)/0.604
e = 2.94 x 10^-3 Volt
(B) I = e / R = 5.07 x 10^-3 A
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