Solenoid and Toroid

Before to know Solenoid and Toroid  , students must know Ampere’s circuital law , proof of Ampere’s circuital law and its application.        To know all these thing click here-

In this topic we will discuss about  one of the application of Ampere’s circuital law . We will define solenoid and Toroid , we will find the magnetic field due to Solenoid and Toroid .

Solenoid

It is the closely wound coil in the form of helix . its length is very large as compared to its diameter.

Magnetic field due to a solenoid

Let current I is flowing through the coil , each turn of solenoid regarded as a circular loop carrying current which produces a magnetic field . Total magnetic field is vector sum of magnetic field due to current through all the turns in the coil .

Let n be the number of turns per unit length of the solenoid . Consider a rectangular loop PQRS  near the middle of the solenoid as shown in figure.

PQ=L . hence total numbers of turn in length L = nL .

The line integral of magnetic field over the closed path PQRS is ,

At a point near the end of the solenoid magnetic field B = μ0nI/2 .

If the solenoid is filled by material of permeability μ in side then magnetic field B = μnI = μ NI/L.

If we draw a plot magnetic field B vs r (distance) from the centre of the solenoid we get the following curve.

Toroid –

Toroid is the endless solenoid in the form of ring . or we can define ‘The toroid is the hollow circular ring on which a large number of insulated turns of a metallic wire are closely wound’. As shown in figure below.

Magnetic field due to current in a toroid–  Let n be the number of turns per unit length of the toroid , I be the current flowing through the toroid . When current passes through the solenoid magnetic field of constant magnitude setup in side the turn of toroid in the form of circular magnetic field . We draw three circle having radii r1,r2 and r3 as shown in fig (b). Let B1 is the magnetic field along loop 1  then using Ampere’s law –

The magnetic field at any point inside the empty space surrounded by toroid or outside the toroid magnetic field is zero .