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Faraday's Law Of Induction - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Faraday's law of induction is considered one the most difficult concept.
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76 Questions around this concept.
Solve by difficulty
The flux linked with a coil at any instant t is given by = 10t2 - 50t + 250. The induced emf (in Volts) at t = 3s is
The figure shows three regions of the magnetic field, each of area A, and in each region magnitude of the magnetic field decreases at a constant rate a. If $\vec{E} $ is an induced electric field then the value of the line integral $\oint \vec{E} \cdot d \vec{r}$ Along the given loop is equal to:
A small circular loop of wire of radius a is located at the center of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I=Io cos (ωt). The emf induced in the smaller inner loop is nearly :
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In the figure shown a square loop PQRS of side 'a' and resistance 'r' is placed near an infinitely long wire carrying a constant current I. The sides PQ and RS are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by 180º about an axis parallel to the long wire and passing through the midpoints of the side QR and PS. The total amount of charge which passes through any point of the loop during rotation is :
The magnetic induction at the centre O in Fig shown is
According to the 'Flemings left hand rule' direction of motion of charge is indicated by the direction of-
When a conducting loop is moved in a magnetic field then the total charge induced depends on -
A conducting circular loop is placed in a uniform magnetic field $0.4 \mathrm{~T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $1 \mathrm{~mm} \mathrm{~s}^{-1}$. The induced emf in the loop when the radius is $5 \mathrm{~cm}$ is:
A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because
(a) the magnetic field is constant.
(b) the magnetic field is in the same plane as the circular coil and it may or may not vary.
(c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably.
(d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.
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Faraday's law of induction
Faraday’s First Law-
Whenever the number of magnetic lines of force (Magnetic Flux) passing through a circuit changes an emf called induced emf is produced in the circuit. The induced emf persists only as long as there is a change of flux.
Faraday’s Second Law-
The induced emf is given by the rate of change of magnetic flux linked with the circuit.
i.e Rate of change of magnetic Flux $=\varepsilon=\frac{-d \phi}{d t}$
where $d \phi \rightarrow \phi_2-\phi_1=$ change in flux
And For N turns it is given as $\varepsilon=\frac{-N d \phi}{d t}$ where $\mathrm{N}=$ Number of turns in the Coil.
The negative sign indicates that induced emf (e) opposes the change of flux. And this Flux may change with time in several ways
I.e As $\phi=B A \cos \Theta$ so $\varepsilon=N \frac{-d}{d t}(B A \cos \Theta)$
1.If Area (A) change then $\varepsilon=-N B \cos \Theta\left(\frac{d A}{d t}\right)$
2.If Magnetic field (B) change then $\varepsilon=-N A \cos \Theta\left(\frac{d B}{d t}\right)$
3. If Angle ( $\theta$ ) change then $\varepsilon=-N A B \frac{d(\cos \Theta)}{d \Theta} \times \frac{d \Theta}{d t}$ or $\varepsilon=+N B A \omega \sin \Theta$
- Induced Current-
$
I=\frac{\varepsilon}{R}=\frac{-N}{R} \frac{d \phi}{d t}
$
where
$R \rightarrow$ Resistance
$\frac{d \phi}{d t} \rightarrow$ Rate of change of flux
- Induced Charge-
$
\begin{aligned}
& d q=i . d t=\frac{-N}{R} \frac{d \phi}{d t} \cdot d t \\
& d q=\frac{-N}{R} d \phi
\end{aligned}
$
I.e Induced Charge time-independent.
- Induced Power-
$
P=\frac{\varepsilon^2}{R}=\frac{N^2}{R}\left(\frac{d \phi}{d t}\right)^2
$
i.e - Induced Power depends on both time and resistance
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