(a) In this situation, the Biot-Savart Law tells us that the magnetic field at t

Question

(a) In this situation, the Biot-Savart Law tells us that the magnetic field at the center of the loop is proportional to the current in the loop multiplied by the length of wire used to make the loop. If this was the only issue determining the field (which it is not) we would expect the field at the center of the 60 cm loop to be larger than that at the center of the 25 cm loop because it takes a longer wire to make the bigger loop. If this was the only issue determining the field, and the two loops had equal currents, we would expect the field at the center of the 60 cm loop to exceed that at the center of the 25 cm loop by what factor?
(b) The other issue determining the field at the center of the loop is the radius of the loop. The Biot-Savart Law tells us that the field is inversely proportional to the square of the radius. If this was the sole issue determining the magnetic field, and the two loops had equal currents, we would expect the field at the center of the 25 cm loop to exceed that at the center of the 60 cm loop by what factor?
(c) If the currents in the two loops are equal, the two issues above determine by what factor the field at the center of one of the loops is larger than the field at the center of the other loop. Taking both issues into account, we should find that the field at the center of the 25 cm loop exceeds that at the center of the 60 cm loop by what factor if they have equal currents? Verify this with the simulation.

Explanation / Answer

a) B = k*I*2*pi*r = k*I*l
B-60/B-25 = 60/25 = 2.4 times
b) B-25/B-60 = 3600/625 = 5.76 times
c) B-25/B-60 = 5.76/2.4 = 2.4 times
B = 2*pi*kI/r
so B-25/B-60 = 2.4

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