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Inductance of solenoid and toroid

What is solenoid?

Solenoid is defined as:”A long tightly wound cylindrical conducting wire is called solenoid.”

Magnetic field due to solenoid: Consider a solenoid having n turns per unit length.When current passes through the solenoid ,magnetic field is produced inside the solenoid which is directed along the axis of solenoid.The magnetic field in space outside the solenoid is so weak that it is considered zero. The inductance of solenoid: A tightly wound cylindrical coil of wire is called solenoid. Relation for inductance of solenoid: Consider a solenoid of length l,area of cross section A having number of turns N.The magnetic field B inside a solenoid carrying  a current i is given as:

B=μi ni —————(1)

Where n is the number of turns per unit length. http://www.physicsabout.com/wp-content/uploads/2016/09/relation-of-inductance-of-solenoid.png


What is toroid?

The solenoid bent into circular shape is called toroid.

Relation for inductance of toroid:

Consider a toroid having rectangular cross sectional area.The inner radius of the toroid is ‘a’ while outer radius is b.The number of turns of toroid is N.Let i be the current flowing through each turn of toroid. The magnetic field lines inside the solenoid is given as:


Where dA = hdr is the area of the elementary strip of toroid .Putting the value of ‘B’ from equation (1) we get:


Which is the relation for inductance of solenoid.The inductance L depends only on geometrical factors.



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