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A flat coil enclosing an area of 0.10 $\mathrm{m}^{2}$ is rotating at 60 $\mathrm{rev} / \mathrm{s}$ , with its axis of rotation perpendicular to a 0.20 $\mathrm{-T}$ magnetic field. (a) If there are 1000 turns on the coil, what is the maximum voltage induced in the coil? (b) When the maximum induced voltage occurs, what is the orientation of the coil with respect to the magnetic field?

a. 7500 \mathrm{V}

b. \text { When the maximum induced voltage occurs, the the normal vector of the coil is parallel to the magnetic field. }

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Cornell University

Rutgers, The State University of New Jersey

Numerade Educator

University of Winnipeg

for part A were asked to figure out the maximum induced voltage in the coil when the number of turns is 1000 and the magnetic field perpendicular to the axis of rotation is point to Tesla. We're told that the area is 0.1 meter squared and it's rotating at 60 revolutions per second, which converted to radiance by multiplying by two. Pi is 376.8 radiance per second. Okay, so the induced voltage will indicate this is part of a is equal to the number of turns in the coil times. The magnetic field time is the area multiplied by Omega times. The sign omega times time. Well, since the sign of a value gives you a number between zero and one, this is maximum when sign of omega T is one. So we can say Max. Yeah, sign omega T equal to one. Therefore, we can say e max is equal to the number of turns multiplied by the magnetic field well supplied by the area well supplied by omega plugging those values and its expression, we find that this is equal to 7.5 times 10 to the third volts or 7.5 kilovolts since 10 to the third is equal to the kill of all weaken box set in as a solution to our question for part A. Now for Part B, it says When the maximum induced voltage occurs, What is the orientation of the coil with respect to the magnetic field? Well, the orientation of the coil with respect to the magnetic field is discussing that sign of omega T term. But again, that's maximum and sign of omega. T is equal toe, um, one. So, since uh, that's true, this has to be at an angle of fada, since if we're considering Omega T to be fada of 90 degrees or the opposite 270 degrees, since that is when the sign of that value is equal to one. So this is when the normal vector of the coil is parallel to the D field with a magnetic field. So let's go back to that page so we can say down here when normal factor of coil is parallel to the magnetic field or the D field. And this is all our solution to part B, so we can go ahead and box all of this in