The magnetic energy stored in an inductor is given by `E=1/2L^(a)l^(b)`. Find the value of `'a'` and `'b'`.
Here `L=` self-inductance `l=` electric current.

Options

A. `a=3, b=0`
B. `a=2, b=1`
C. `a=0, b=2`
D. `a=1, b=2`

Explanation

(d) `E=1/2 L^(a)l^(b)`
`[E]=[ML^(2)T^(-2)],[L]=[ML^(2)T^(-2)A^(-2),[l]=[M^(0)L^(0)T^(0)A]`
Using principle of Homogeneity,
`[ML^(2)T^(-2)]=[M^(1)L^(2)T^(-2)A^(-2)]^(a)[M^(0)L^(0)A]^(b)`
`[MLT^(-2)]=[M^(a)L^(2a)T^(-2a)A^(l=2a+b)]`
`implies a=1` and `=-2a+b=0impliesb=2`