Question
The magnetic flux $$\phi $$ linked with a conducting coil depends on time as $$\phi = 4{t^n} + 6,$$ where $$n$$ is a positive constant. The induced emf in the coil is $$e.$$ Then which is wrong?
A.
If $$0 < n < 1,\,e \ne 0$$ and $$\left| e \right|$$ decreases with time
B.
If $$n = 1,$$ $$e$$ is constant
C.
If $$n > 1,\left| e \right|$$ increases with time
D.
If $$n > 1,\left| e \right|$$ decreases with time
Answer :
If $$n > 1,\left| e \right|$$ decreases with time
Solution :
$$\eqalign{
& \phi = 4{t^n} + 6 \cr
& \frac{{d\phi }}{{dt}} = 4n{t^{n - 1}} \cr
& \left| e \right| = 4n{t^{n - 1}},\left| e \right| = \frac{{4n}}{{{t^{1 - n}}}} \cr} $$