Question

The flux of magnetic field through a closed conducting loop changes with time according to the equation,$\Phi ={at}^2+bt+c$.$\left(a\right)$ Write the $SI$ units of $a,b$ and $c$ $\left(b\right)$ If the magnitudes of $a,b$ and $c$ are $0\cdot 20,0.40$ and $0.60$ respectively, find the including emf at $t=2s$.

Answer 1

Given:

$\Phi ={at}^2+bt+c$
Same dimensional quantity can be added, subtracted and equated.

(a) $a=\left[\frac{\varphi }{t^2}\right]=\left[\frac{\varphi /t}{t}\right]=\frac{volt}{sec};b=\left[\frac{\varphi }{t^{}}\right]=volt;c=\left[\varphi \right]=Weber$

(b) $a=0.2,b=0.4,c=0.6,t=2s$
$E=\frac{d\varphi }{{dt}^{}}=2at+b=2\times 0.2\times 2+0.4=1.2volt$