A toroidal solenoid has a mean radius of 10.0 cm and a crosssectional area of 4.00 cm^2 and is

step 1 Hi in the given problem mean radius of toroidal solenoid is given as r is equal to 10 .0 centime

A toroidal solenoid has a mean radius of 10.0 cm and a...

A toroidal solenoid has a mean radius of $10.0 \mathrm{~cm}$ and a crosssectional area of $4.00 \mathrm{~cm}^{2}$ and is wound uniformly with 100 turns. A second coil with 500 turns is wound uniformly on top of the first. What is the mutual inductance of these coils?

Key Concepts

Mutual Inductance

Mutual inductance is a measure of how effectively a change in current in one coil induces an electromotive force (emf) in another. It depends on the geometry of the coils and their relative positions, and is defined by the ratio of the total magnetic flux linking the secondary coil to the current in the primary coil.

Magnetic Flux

Magnetic flux quantifies the amount of magnetic field passing through a given surface area. In the context of inductance, it illustrates how the magnetic field produced by one coil links with another, with the effective flux being proportional to both the magnetic field strength and the cross-sectional area of the coil.

Toroidal Solenoid

A toroidal solenoid is a coil of wire wound in the shape of a torus (doughnut-shaped). Its geometry causes the magnetic field to be largely confined within the core of the toroid, making it an ideal configuration for high inductance and reduced external magnetic interference. Analysis of its magnetic field typically employs Ampere’s law due to its symmetry.

Ampere’s Law

Ampere’s law relates the magnetic field in a closed loop to the electric current that it encloses. In the analysis of coils, especially those with symmetric configurations like toroids, Ampere’s law is used to derive expressions for the magnetic field intensity, which then plays a central role in calculating the magnetic flux and thus the mutual inductance.

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