Question

The energy stored in the magnetic field if current of $5\text{A}$ produces a magnetic flux of $2\times {10}^{-3}\text{Wb}$ through a coil of $500$ turns is

​​​​​​​$[$1 Mark$]$

• A. $2.5\text{J}$
• B. $0.25\text{J}$
• C. $250\text{J}$
• D. $1.5\text{J}$

Answer 1

The correct option is A $2.5\text{J}$

Accordding to Faraday's law,

$\epsilon =-N\frac{d\varphi }{dt}$

$\varphi \to$ Flux linked with each turn of coil

$N\to$ Total number of turns

By self induction, $\epsilon =-L\frac{di}{dt}$

Comparing both expression

$N\frac{d\varphi }{dt}=L\frac{di}{dt}$

$:N\varphi =LI$ ( when $i=0,\varphi =0$ )

$L=\frac{N\varphi }{I}=\frac{500\times 2\times {10}^{-3}}{5}=0.2\text{H}$

Energy stored,

$U_m=\frac{1}{2}L{I}^2=\frac{1}{2}\times 0.2\times (5{)}^2=2.5\text{J}$