If magnetic flux $\phi = (3t^2 - 2t + 5) \ Wb$,then what is the induced emf at $t = 2 \ s$?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(10 V) According to Faraday's law of electromagnetic induction,the induced emf $\varepsilon$ is given by $\varepsilon = -\frac{d\phi}{dt}$.
Given $\phi = 3t^2 - 2t + 5$.
Differentiating with respect to $t$,we get $\frac{d\phi}{dt} = \frac{d}{dt}(3t^2 - 2t + 5) = 6t - 2$.
The magnitude of induced emf is $|\varepsilon| = |6t - 2|$.
At $t = 2 \ s$,$|\varepsilon| = |6(2) - 2| = |12 - 2| = 10 \ V$.

Explore More

Similar Questions

$A$ physicist works in a laboratory where the magnetic field is $2 \, T$. She wears a necklace enclosing an area of $0.01 \, m^2$ in such a way that the plane of the necklace is normal to the field,and it has a resistance $R = 0.01 \, \Omega$. Because of a power failure,the magnetic field decays to $1 \, T$ in $10^{-3} \, s$. What is the total heat produced in her necklace in Joules?

$A$ metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t = 0$ and completely emerges out at $t = T \, \text{sec}$. The current in the ring varies as

The working of a dynamo is based on the principle of

Two identical circular coils $A$ and $B$ are kept on a horizontal tube side by side without touching each other. If the current in the coil $A$ increases with time,in response,the coil $B$

$A$ magnet is moved in the direction indicated by an arrow between two coils $AB$ and $CD$ as shown in the figure. The direction of the induced current in the coils is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo