Question 219: Electromagnetic Induction

Question

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?

Accepted Answer

We need to find the phase difference between the
flux linked
with a rotating coil in a uniform magnetic field and the
induced emf
.
Step 1: Expression for flux linkage
If a coil of $N$ turns and area $A$ rotates in a uniform magnetic field $B$ with angular speed $\omega$, the flux linked at time $t$ is:
$ \phi(t) = NBA \cos(\omega t) $
Step 2: Expression for induced emf
Induced emf is given by
FaradayÃ¢ÂÂs law
:
$ e(t) = - \frac{d\phi}{dt} $
So,
$ e(t) = -\frac{d}{dt}\big[NBA \cos(\omega t)\big] $
$ e(t) = NBA\omega \sin(\omega t) $
Step 3: Compare phase
Flux $\phi(t) = \cos(\omega t)$
emf $e(t) = \sin(\omega t)$
We know:
$ \sin(\omega t) = \cos\Big(\omega t - \frac{\pi}{2}\Big) $
So, the induced emf
lags
the flux by $\pi/2$. Equivalently, flux leads emf by $\pi/2$.
Ã¢ÂÂ Final Answer:
The phase difference between flux and induced emf is:
$ \boxed{\frac{\pi}{2}} $
Correct Option: D

Answer

$\pi$

Answer

$-\frac{\pi}{6}$

Answer

$\frac{\pi}{3}$

Answer

$\frac{\pi}{2}$

Electromagnetic Induction

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?

Choose the correct answer: