Question

The magnetic flux through a coil perpendicular to its plane and directed into paper is varying according to the relation $\varphi =(2t^2+4t+6)mWb$. The emf induced in the loop at $t=4s$ is

• A. $0.12V$
• B. $2.4V$
• C. $0.02V$
• D. $1.2V$

Answer 1

Answer: (C)

$0.02V$

Given: The magnetic flux through the coil is given by $\varphi =(2t^2+4t+6)mWb$.

To find: The EMF induced in the loop at $t=4s$.
The EMF induced in the loop due to the flux through it is given as:

$ϵ=\frac{d\varphi }{dt}=\frac{d}{dt}(2t^2+4t+6)\times {10}^{-3}Wb{s}^{-1}$

$=(4t+4)\times {10}^{-3}$

The induced EMF at t=4s is obtained by substituting the value of time.

$ϵ=(4\times 4+4)\times {10}^{-3}V$
$=20\times {10}^{-3}V$

$⟹0.02V$

Option $\left(C\right)$ is correct.