Derive an expression for the field due to a toroid using Ampere's circuital law
Answers
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Explanation:
A solenoid is a long wire wound that carries current in the shape of a close-packed helix. A large number of isolated copper wire turns are wounded on a cylindrical tube of cardboard or china clay to create a solenoid. A magnetic field is produced inside the solenoid when an electrical current is passed through the solenoid.
If the solenoid is long and there are no gaps in the successive isolated copper turns, then the solenoid's magnetic field is uniform; with virtually no magnetic field outside. The explanation is that a large number of circular current elements can form the solenoid. The magnetic field is along its axis because of a circular loop and the current is equal and opposite in the upper and lower straight portions of the solenoid. Because of this, the magnetic field perpendicular to the solenoid axis is zero and therefore the resulting magnetic field is located along the solenoid axis. Thus,
B = μ0nI
If there are N turns in the length l of wire, then
n = N/l or B = μ0NI/ld