Inductor :
Already we have studied about capacitor – that stores energy in the form of electric field. Like capacitor, inductor is also quite a commonly used element in electric circuits, which stores magnetic energy. Inductance of an inductor depends on its geometry and medium in which it lies.
As we know that when current flows through a conductor a magnetic field is set-up around it, and hence it is associated with magnetic flux.
If magnetic flux associated with a coil is φ and current in it is I , then φ= LI , & the expression L = φ/I , Where ‘ L ‘ is called self-inductance of the coil.
S.I. unit of inductance is henry.
Self Induction :
Consider the circuit, in which a solenoid is connected across a cell through a resistor.
When switch is open current in the circuit is zero. When switch is closed current flows in it. Since current in the circuit increases from zero to a certain value, magnetic field associated with it changes that causes induction of an e.m.f. in the solenoid.
Induction of an e.m.f. due to variation of current in the coil itself is known as self induction.
Since , φB = LI ;
$ \displaystyle \xi = -\frac{d\phi}{dt} = -\frac{d(L I)}{dt} $
$ \displaystyle \xi = -L \frac{d( I)}{dt} $
Self inductance of an ideal solenoid
Let current I flows through a solenoid. Magnetic field due to solenoid is
B = μ0nI , where n is the number of turns per unit length.
If area of cross section of the solenoid is A then flux associated with length l is equal to φ = nlBA .
where l is the length of the solenoid. Now B = μ0nI
$ \displaystyle L = \frac{\phi}{I} = \frac{n l B A}{I} $
$ \displaystyle L = \frac{nl (\mu_0 n I A)}{I} $
$ \displaystyle L = \mu_0 n^2 l A $