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Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their...

Helmholtz coils are frequently used in experiments because they create a uniform magnetic field about their central axis. 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. Suppose the radius of the coils is ?=16.50 cm R=16.50 cm and each coil carries a current of ?=15.50 AI=15.50 A and has ?=500.0 turns.N=500.0 turns. The coils are in the ??yz plane where one coil's center is at ?=0 x=0 the other coil's center is at ?=?.x=R.

Using the Biot–Savart law, determine 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, ?0.

Bx= ?

Evaluate the magnetic field ??Bx at ?=4.125 cm x=4.125 cm (14?)(14R) and ?=12.38 cm x=12.38 cm (34?).

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genius_generous answered 3 months ago
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