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Moving Charges And Magnetism

Question

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What is the toroid? Using Ampere's circuital law calculate the magnetic field inside the toroid.

Solution

When a solenoid is in the form of a ring then it is treated as toroid. Toroid is basically, a hollow circular ring on which a large number of turns of wire are closely wound.

Consider a toroid carrying current I and has N turns. The magnetic field is set up inside the turns of the toroid. The magnetic lines of force inside the toroid are concentric circles.
By symmetry the magnitude of the field

\vec{B}

is same at all points on the circle of radius r and is directed tangentially to the circle at any point.

∴

\oint \vec{B} . \vec{dl} = \oint B dl cosθ °

\oint \vec{B} . \vec{dl} = \oint B dl \cos 0 °

\oint \vec{B} . \vec{dl} = B 2 πr

By applying Ampere's circuital law,

\oint \vec{B} . \vec{dl} = μ_{0} \times total current passing through circle of radius r . B 2 πr = μ_{0} \times N \times 2 πrl

∴

B = μ_{0} NI

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

Answer the following questions:
A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

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