A toroid having a square cross section, 5.00 cm on a side, and an inner radius of 15.0 cm has

step 1 Part A of the given problem, the inner radius R is equal to 15 centimeter. So the field there is

A toroid having a square cross section, 5.00 cm on a side,...

A toroid having a square cross section, $5.00 \mathrm{~cm}$ on a side, and an inner radius of $15.0 \mathrm{~cm}$ has 500 turns and carries a current of 0.800 A. (It is made up of a square solenoid - instead of a round one as in Fig. $29-17$ - bent into a doughnut shape. ) What is the magnetic field inside the toroid at (a) the inner radius and (b) the outer radius?

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Key Concepts

Ampere's Circuital Law

This law is a fundamental principle in magnetostatics that relates the magnetic field around a closed loop to the net current passing through the loop. It is crucial for calculating the magnetic field in devices with high symmetry such as toroids, as it allows one to set up an integral of the magnetic field along a chosen path and equate it to ?? times the enclosed current.

Toroidal Coil

A toroid is a coil of wire in the shape of a doughnut, where the turns are wound around a circular ring. This configuration results in a magnetic field that is largely confined within the core of the toroid. The application of Ampere’s Law to a toroid, with its symmetry, simplifies the calculation of the magnetic field inside, turning it into a function of the number of turns, current, and the mean radius of the toroid.

Magnetic Field Variation with Radius

In a toroid, the magnetic field is not uniform across the cross section; it changes with the distance from the center. Specifically, the field strength varies inversely with the radius (B ? 1/r), meaning that at different radii (e.g., inner versus outer surfaces), the magnetic field will have different magnitudes. This concept is essential when evaluating the magnetic field at various positions within the toroid's cross section.

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