where N is the number of revolutions of the toroidal coil, I is the amount of current flowing and r is the radius of the toroid. The magnetic field of a toroid is calculated by applying the law of the ampere circuit. The principle of operation of the magnet and toroid is based on electromagnetism. This is one of the similarities between the two. However, there is a difference between magnet and toroidal because for a given toroidal coil, the amount of electric current is greater than the solenoid, so they are the same size. The toroid formula is used to calculate the number of revolutions in a toroidal coil. The torus is an example of a toroid, which is the surface of a donut. Donuts are an example of a solid torus created by the rotation of a disc and should not be confused with toroids. A toroid is shaped like a magnet that is bent into a circular shape to close in a loop-like structure. The toroid is a hollow circular ring, as seen in the image below, with many coils of enamelled wire, tightly wound with a negligible distance between any two turns. The figure above is a pictorial representation of the cross-sectional view of the inner radius of the toroid and wire. The term toroid is also used to describe a toroidal polyhedron.

In this context, a toroid does not need to be circular and can have any number of holes. A g-hole toroid can be thought of as an approximation of the area of a torus of the topological genus, g, of 1 or more. The Euler characteristic χ of a g-hole toroid is 2(1-g).  To learn more about Toroid, click on the video below. In a toroid, all the magnetic flux is contained in the material of the core. This is because the kernel has no ends from which the flow could escape. Flux confinement prevents external magnetic fields from affecting the behavior of the toroid, and also prevents the magnetic field in the toroid from affecting other components of a circuit. The volume (V) and the area (S) of a toroid are given by the following equations, where A is the area of the square section of the side and R is the radius of revolution.

In mathematics, a toroid is a rotating surface with a hole in the middle. The axis of rotation passes through the hole and therefore does not intersect the surface.  For example, rotating a rectangle around an axis parallel to one of its edges creates a hollow rectangular ring. If the rotated figure is a circle, then the object is called a torus. Consider a hollow circular ring with many turns of the live wire wrapped around it. In the figure above, the magnetic field B is present at point P, which is located inside the toroid. In the figure above, the loop is thought of as an amperius loop forming a circle passing through the P point, resulting in concentric circles inside the toroid. The magnetic field due to a toroid can be specified as follows: A toroid is indicated by the velocity radius R, measured from the center of the rotated cross-section.

For symmetrical sections, the volume and area of the body can be calculated (with circumference C and area A of the section): The first toroid was invented in 1830 by physicist Michael Faraday. He noticed that the change in the magnetic field led to the voltage in a wire. This phenomenon is known as Faraday`s law of induction. The magnetic field of a living toroid is independent of the radius. Indeed, the magnetic field of the toroid is given by B = μonI, where n is the number of revolutions, I is the electric current and μo is the permeability. A toroid can be thought of as a circular magnet used in an electrical circuit, as a low-frequency inductor when large inductors are required. A toroid has more inductance for a certain number of turns than a magnet with a core of the same material and similar size. This makes it possible to build highly inductive coils of appropriate physical size and mass. Toroidal coils with a given inductor can carry more current than solenoids of similar size because larger diameter wires can be used and the total amount of wire is less, which reduces resistance. A toroid is a spool of insulated or enamelled wire wound on a mold shaped like a powdered iron fritter. A toroid is used as an inductor in electronic circuits, especially at low frequencies where relatively large inductors are required.