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Byju's Answer
Standard XII
Physics
Coupling
Define self-i...
Question
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
2
L
I
2
.
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Solution
Self inductance
is defined as the
induction
of a voltage in a current-carrying wire when the current in the wire itself is changing.
The potential difference across an inductor with rate of change of current
d
I
d
t
across it is
V
=
L
d
I
d
t
Hence work done to build up current
I
=
∫
V
d
q
=
∫
I
0
(
L
d
I
d
t
)
(
I
d
t
)
=
1
2
L
I
2
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