The magnetic flux through a loop is varying according to a relation $\phi = 6t^2 + 7t + 1$ where $\phi$ is in milliweber and t is in second. What is the e.m.f. induced in the loop at t = 2 second?

The magnetic flux through a loop is varying according to a relation φ = 6t² + 7t + 1 where φ is in milliweber

Question 28 of 48

\phi = 6t^2 + 7t + 1

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2017Subjective· 2mImportance★★★★★

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Induced emf is the negative rate of change of flux: $\varepsilon = -d\phi/dt$ .

By Faraday's law of electromagnetic induction, the induced emf is

$\varepsilon = -\frac{d\phi}{dt}$

Given $\phi = 6t^2+7t+1$ (in milliweber, $t$ in seconds):

$\frac{d\phi}{dt} = 12t+7 \quad(\text{mWb/s} = \text{mV})$

At $t=2\ \text{s}$ :

$\frac{d\phi}{dt} = 12(2)+7 = 24+7 = 31\ \text{mV}$

$\varepsilon = -31\ \text{mV}$

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