This question asks us to use Biot Savart. Starting from the Biot-Savart law, sho

Question

This question asks us to use Biot Savart.

Starting from the Biot-Savart law, show that the magnitude of the magnetic field on the axis of a circular loop of radius R a distance z away is given by: (This part should be done after you have done question 3 for the prelab in the workbook). Define the non-uniformity of a field near a point x be related to the power of deltax the field changes by when moved a small distance deltax away from a x. for example B(z) = A+C(z-x) is less uniform than B(z)=A+D(z-x)2, since when z = x + deltax, the first field differs from A by deltax whereas the second differs from A by deltax2, deltax2 is smaller, since I am considering small displacement from x. Suppose the current coils in Helmholtz coils are separated by a distance d rather than R. Is there a difference in the uniformity of the field near the midpoint of the two current coils when this change is made? (Hint: you may need the expansion (1 + epsilon)alpha 1+ alpha epsilon+1/2(alpha-1) alpha epsilon2+1/6(alpha-2)( alpha-1) alpha epsilon3+1/24(alpha-3)( alpha-2)( alpha-1) alpha epsilon4. Figure out how much of an effect a small displacement on axis from the midpoint has on the magnitude of the field at that point.)

Explanation / Answer

A current carrying wire generates a magnetic field. According to Biot-Savart

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