Question

Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their axial direction.
Ma Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their axial direction. For example, they are traditionally used in the experiment for the measurement of the charge to mass ratio of the electron. Helmholtz coils are two coils separated by a distance equal to their radius and also carry equal currents in the same direction, as shown in the figure on the right. Suppose the radius of the coils is 12.00 cm, each coil carries a current of 11.00 A and have 360.0 turns. The coils are in the yz plane where one coil's center is at x 0 the other coil's center is at x R. Using the Biot-Savart law, what is the expression for the resultant magnetic field, Bx, along the line x joining their centers Express the magnetic field in terms of the radius of the coils R, the number of turns N, the current I, x, and the permeability of free space, Ho (Scroll down for more questions.)

Answer 1

Given value Given data Radius R = 12.00 N Number of turn N = 360 Current in each turn i = 11.00 Magnetics field done to a single coil or radius R, coil turn N, x form the current or coil is B vector = (40/4 pi) (2 i pi R^2/(R^2 + x^2)^3/2) x^^B vector = 10/4 pi (2i pi (12)^2/(12^2 + 0^2)^3/2) times (0) B vector = 0 Using the above expression Resultant magnetic field due to the two coils of Helmthoriz coil in Bx = (u0/v pi) (2 Ni pi R^2) (x^^/(R^2 + x^2)^3/2 + x^^/R^2 (x - R)^2)^3/2 at = x = (3.000) (R/N) Bx = 16.12 times 10^-3 x T at x = (9.00) (3R/N) Bx = 16.12 10^-3 xT