Two circular coils with radius a, each wound with N turns of wire carrying a current I, circulating in the same direction in both coils. The coils are separated by a distance a equal to their radii. In this configuration the coils are called Helmholtz coils; they produce a very uniform magnetic field in the region between them.
a) Derive the expression for the magnitude B of the magnetic field at a point on the axis a distance x to the right of point P, which is midway between the coils.
1. B=?0NIa22(1((x+a/2)2+a2)3/2+1((x?a/ 2)2+a2)3/2)
2. B=?0NIa22(1((x+a/2)2+a2)3/2?1((x?a/ 2)2+a2)3/2)
3. B=?0NIa22(1((x+a/2)2?a2)3/2+1((x?a/ 2)2?a2)3/2)
4. B=?0NIa22(1((x+a/2)2?a2)3/2?1((x?a/ 2)2+a2)3/2)
b) From part (a), obtain an expression for the magnitude of the magnetic field at point P.
Express your answer in terms of the variables N, I, a, and appropriate constant (?0).
c) Calculate the magnitude of the magnetic field at P if 310 turns, I = 5.00 A , and a = 8.00 cm
d) Calculate dB/dx at P(x=0).
e) Calculate d2B/dx2 at P(x=0).