Solenoid and Toroid

What is Solenoid?

Let us consider a solenoid, such that its length is large as compared to its radius. Here, the wire is wound in the form of helix with very little gap between any two turns. Also, the wires are enameled, thus rendering them insulated from each other. As a result, each turn can be taken as a closed circular loop. The magnetic field thus generated is equivalent to that generated by a circular loop and the total magnetic field generated by the solenoid can be given as the vector sum of force generated by each such turn. The magnetic field lines generated inside a finite solenoid has been shown in the figure below.
solenoid

We can see from the figure that the magnetic field inside the solenoid is uniform in nature and is along the axis of the solenoid. The field at the exterior at any point immediate to the solenoid is very weak and the field lines cannot be seen near the close vicinity. It is important to note that the field inside it is parallel to its axis at every position.

From the Ampere’s Law, the magnetic force produced by a solenoid can be given as,

1.1.2

Where n is the number of turns of the wire per unit length, I is the current flowing through the wire and the direction is given using the right-hand thumb rule.

What is Toroid?

A toroid is shaped like a solenoid bent into a circular shape such as to close itself into a loop-like structure. The toroid is a hollow circular ring, as can be seen in the image shown below, with large number of turns of enameled wire, closely wound with negligible spacing between any two turns.

toroid

The magnetic field inside and outside the toroid is zero. The magnetic field inside the toroid, along the circular turn, is constant in magnitude and its direction inside the toroid is clockwise as per the right-hand thumb rule for circular loops.

The magnetic field due to a toroid can be given as,

1.1.1

Where N is the number of turns of the toroid coil, I is the amount of current flowing and r is the radius of the toroid.

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Magnetic induction is a