Question

Show steps.

Problem 5 (25pts). A Helmholtz coil (see figure below) is a structure used for creating uniform magnetic fields at the centre. Consider two thin circular coaxial coils each of radius R, having N turns, carrying a current I in the same direction and separated by a distance d. The field due to the thin wire connecting the two coils can be ignored a) Find the magnetic field B on the axis of symmetry (the r-axis) of the Helmholtz coil. b) Show that at the point midway between the two coils c) Show that if d = R, 을 = 0 at the point midway between the two coils. d) Explain what your previous results in b) and c) mean. dB

Answer 1

Given that A Helmholtz coil consider a circular coil of one turn as shown in fig According to Boil savant law, magnetic field at a point p on the axis of car consider two small element of coil each of length at c and D which are situated at opposite edges pc = partial differential = r = squareroot R^2 + x^2 alpha beta^1 = alpha beta = mu_0 I dl/4 pi r^2 = mu_0 I dl/4 pi (R^2 + x^2) alpha beta cos phi cancle with alpha beta cos phi^1 so, we just have to integrated alpha beta sin phi B = integral alpha beta sin phi = integral mu_0 Id l/4 pi (R^1 + x^2) sin phi = mu_0 I/4 pi (R^2 + x^2) sin phi integral dl also sin phi = R/squareroot R^2 + x^2 B = mu_0 I/4 pi (R^2 + x^2)