What is the phase difference between the flux | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The magnetic flux linked with a coil rotating in a uniform magnetic field is given by $\phi = BA \cos(\omega t)$,where $B$ is the magnetic field,$

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(D) The magnetic flux linked with a coil rotating in a uniform magnetic field is given by $\phi = BA \cos(\omega t)$,where $B$ is the magnetic field,$A$ is the area of the coil,and $\omega$ is the angular velocity.According to Faraday's law of electromagnetic induction,the induced e.m.f. is given by $\epsilon = -\frac{d\phi}{dt}$.Substituting the expression for $\phi$,we get $\epsilon = -\frac{d}{dt} [BA \cos(\omega t)] = BA\omega \sin(\omega t)$.Using the trigonometric identity $\sin(	heta) = \cos(	heta - \frac{\pi}{2})$,we can write $\epsilon = BA\omega \cos(\omega t - \frac{\pi}{2})$.Comparing the phase of the flux $(\omega t)$ and the phase of the induced e.m.f. $(\omega t - \frac{\pi}{2})$,the phase difference is $\frac{\pi}{2}$.

What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?

Similar Questions

$A$ rectangular loop circuit has a sliding wire $PQ$ as shown in the figure. The loop is placed in a magnetic field $B$,perpendicular to its plane. The resistance of the wire $PQ$ is $R$. If the wire moves with constant velocity $v$,then find the current flowing in the wire $PQ$?

$A$ horizontal loop $abcd$ is moved across the pole pieces of a magnet as shown in the figure with a constant speed $v$. When the edge $ab$ of the loop enters the pole pieces at time $t = 0 \text{ s}$,which one of the following graphs correctly represents the induced emf in the coil?

$A$ conducting rod $PQ$ of length $5\,m$ oriented as shown in the figure is moving with velocity $(2\,m/s)\hat{i}$ without any rotation in a uniform magnetic field $(3\hat{j} + 4\hat{k})\,T$. The $Emf$ induced in the rod is.....$V$.

Two metallic rings of radius $R$ are rolling on a metallic rod. $A$ magnetic field of magnitude $B$ is applied in the region. The magnitude of the potential difference between point $A$ and point $C$ on the two rings (as shown) will be:

The current-carrying wire and the rod $AB$ are in the same plane. The rod moves parallel to the wire with a velocity $v$. Which one of the following statements is true about the induced emf in the rod?

Vedclass Test Series

Exam Paper Generator

Online Exam Module