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Electrostatic Potential And Capacitance

Question
CBSEENPH12039074

Define self-inductance of a coil. Show that magnetic energy required to build up the current I in a coil of self-inductance L is given by 1 half LI squared

Solution

 Self-inductance of a coil is numerically equal to the magnetic flux linked with the coil when the current through coil is one Ampere.

Mathematically, it is given by, 
                                               straight phi straight space equals straight space LI

where, L is the constant of proportionality and is called the self-inductance.

Energy stored in an inductor:

Consider a source of emf connected to an inductor L.

With increase in current, the opposing induced emf is given by, straight e straight space equals straight space minus straight L di over dt
If the source of emf sends a current i through the inductor for a small time dt, then the amount of work done by the source, 
dW straight space equals vertical line straight e vertical line straight i straight space dt straight space equals straight space Li    di over dt dt straight space equals straight space Li straight space di
Hence, the total amount of work done by source of emf when the current increases from its initial values (i = 0) to its final value (I) is given by,
Error converting from MathML to accessible text.
This work done gets stored in the inductor in the form of energy.
Therefore comma space Energy space stored space in space the space magnetic space inductor comma space straight U space equals 1 half LI squared

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