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# A magnetic field of magnitude 0.300 T is oriented perpendicular to the plane of a circular loop. (a) Calculate the loop radius if the magnetic flux through the loop is 2.70 Wb. (b) Calculate the new magnetic flux if the loop radius is doubled.

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we're told that we have in the magnetic field of a value off 0.3 Tesla and ah, it's oriented perpendicular. So data here is equal to zero degrees to the plane of a circular loop, and it wants us to find the radius of the loop. If the magnetic flux is point is 2.7 for part A. So we have a value of magnetic flux. We're told that fi is equal to two 0.7. Okay, So since the equation for the flux is a magnetic field times the area times the co sign of the angle fada. But here, if they do, zero co sign of zero is one. So this is magnetic field times the area which is pi r squared. So solving for are we find that the radius is equal to the square root of the flux divided by the magnetic field times pi. So plugging those values into this expression, we find that the radius is equal to one 0.69 on the units. Here are meters making box. It in is their solution. For part a part B says, calculate the new magnetic flux if the radius is now doubled Okay, So for part B, we're going to say that the magnetic flux here, the new one will call it five. Prime is equal to the magnetic field times pi times are prime The new radius. Sorry about that. It's fixed that so our prime squared where our prime is the new radius. It's equal to two R and then again, time to the coastline of Fada. They just still zero. So this is multiplied by one so we don't worry about that. So this is the magnetic feel climbs pie. And then again, our prime is equal to two times the original radius that we calculated in part a. So plugging all those values into this expression, we find that this is equal to 10.76 making box said it is the solution to your question.

University of Kansas