Question

The magnetic flux $\varphi$ linked with a conducting coil depends on time as $\varphi =4t^n+6$, where $n$ is a positive constant. The induced emf in the coil is $e$.

• 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
• E. answer required

Answer 1

Answer: (A), (B), (C)

The correct options are
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

Faraday's Law states:

$ϵ=-\frac{d\varphi }{dt}$

$ϵ=-4n{t}^{n-1}$

if $n=1$, $|e|=4$

if $n>1$, $|e|=4n{t}^{n-1}$

if $n-1>1$, then $e$ increases

else if $n-1<1$, e decreases