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Question 11 Mark
A long straight current carrying wire passes normally through the centre of circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify.
Answer
No, As the magnetic field due to current carrying wire will be in the plane of the circular loop, so magnetic flux will remain zero.
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Question 21 Mark
What is the direction of induced currents in metal rings 1 and 2 when current I in the wire is increasing steadily?
Answer
Clockwise in loop 1
Anticlockwise in loop 2
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Question 31 Mark
A conducting loop is held below a current carrying wire PQ as shown. Predict the direction of the induced current in the loop when the current in the wire is constantly increasing.
Answer
Anticlockwise.
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Question 41 Mark
A bar magnet is moved in the direction indicated by the arrow between two coils PQ and CD. Predict the direction of the induced current in each coil.
Answer
Q to P through ammeter and D to C through ammeter.
Alternate answer
(Anticlockwise as seen from left in coil PQ clockwise as seen from left in coil CD)
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Question 51 Mark
Define the term self-inductance of a solenoid. Obtain the expression for the magnetic energy stored in an inductor of self-inductance L to build up a current I through it.
Answer
Self inductance: It is equal to the magnetic flux, linked with the solenoid, when a unit current passes through it.
Alternate Answer
It is equal to the induced emf in the solenoid when the current, through the solenoid itself, changes at a unit rate.
Energy stored:
$\text{U}=\int_o^IEidt$
Here $|\text{E}|=L\frac{di}{dt}$
$U=\therefore\text{U}=\int_o^lL\frac{di}{dt}\times{idt}=\int_o^I\ Lidi$
$\therefore \text{U}=\frac{1}{2}LI^2$
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Question 61 Mark
Predict the polarity of the capacitor in the situation described below:
Answer
A is positive and B is negative.
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Question 71 Mark
The motion of copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?
Answer
As the plate oscillate, the changing magnetic flux through the plate produces a strong eddy current in the direction, which opposes the cause. Also, copper being diamagnetic substance, it gets magnetised in the opposite direction, so the plate motion gets damped.
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Question 81 Mark
How does the mutual inductance of a pair of coils change when
  1. Distance between the coils is increased and
  2. Number of turns in the coils is increased?
Answer
  1. Mutual inductance decreases.
  2. Mutual inductance increases.
Concept:
  1. If distance between two coils is increased as shown in figure,

It causes decrease in magnetic flux linked with the coil $C_2$. Hence induced emf in coil $C_2$ decreases by relation$\varepsilon_{2} = \frac{-\text{d}\varphi_{2}}{\text{dt}}$. Hence mutual inductance decreases.
  1. From relation $M_{21}=\mu_{0}\ n_1\ n_2$ Al, if number of turns in one of the coils or both increases, means mutual inductance will increase.
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Question 91 Mark
A bar magnet is moved in the direction indicated by the arrow between two coils PQ and CD. Predict the directions of induced current in each coil.

Answer
Clock wise in both coils/Direction of Current is from P$\rightarrow$Q and C$\rightarrow$D.
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Question 101 Mark
Mention the two characteristic properties of the material suitable for making core of a transformer.
Answer
  1. Low Coercivity/Low Retentivity.
  2. Low hysteresis loss.
  3. HighMagnetic Susceptibility/High Permeability.
  4. High resistivity.
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Question 111 Mark
Two bar magnets are quickly moved towards a metallic loop connected across a capacitor 'C' as shown in the figure. Predict the polarity of the capacitor.
Answer
Upper plate is positive and lower plate is negative.
Alternate Answer
Upper plate is negative and lower plate is positive.
(because axis is not given)

Alternate Answer
Accept diagrammatic answer also.
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Question 121 Mark
Define self-inductance of a coil. Write its S.I. unit.
Answer
Magnetic flux linked through a coil when current flowing through is unity./ Induced emf in a coil when current is changing at the unit rate. SI unit is henry.
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Question 131 Mark
Give one example of use of eddy currents.
Answer
Any one of the following:
  1. Magnetic braking in trains.
  2. Electromagnetic damping in certain galvanometers.
  3. Induction furnace to produce high temperature.
  4. Electric power meters (in which the disc rotates due to eddy currents.)
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Question 141 Mark
Predict the directions of induced currents in metal rings 1 and 2 lying in the same plane where current I in the wire is increasing steadily.
Answer
  1. Clockwise in 1.
  2. Anticlockwise in 2.
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Question 151 Mark
A plot of magnetic flux ($\Phi$) versus current (I) is shown in the figure for two inductors A and B. Which of the two has larger value of self inductance?
Answer
Line A.
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Question 161 Mark
Two circular loops are placed with their centres separated by a fixed distance. How would you orient the loops to have:
  1. The largest mutual inductance.
  2. The smallest mutual inductance?
Answer
  1. When the loops have their axis at 0' the mutual inductance is maximum.
  2. When loops have their axis at 90' then their inductance is minimum.
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Question 171 Mark
Why does a metallic piece become very hot when it is surrounded by a coil carrying high frequency alternating current?
Answer
Due to flow of high frequency alternating current in the coil, the magnetic flux linked with the metallic piece changes by a large amount, so heavy eddy currents are induced in the metallic piece. These currents cause metallic piece to get heated.
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Question 181 Mark
How does the self-inductance of an air coil change, when:
  1. The number of turns in the coil is decreased?
  2. An iron rod is introduced in the coil?
Answer
  1. Self-inductance of a $\text{coil} \propto \text{N}_2.$
When number of turns in coil is decreased, the self-inductance will decrease.
  1. When an iron rod is introduced in the coil, the self-inductance of coil increases.
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Question 191 Mark
Consider the self-inductance per unit length of a solenoid at its centre and that near its ends. Which of the two is greater?
Answer
Self inductance depends upon length of solenoid.
As inductance is greater at center as induction at center is due to both ends.
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Question 201 Mark
Give the direction in which the induced current flows in the coil mounted on an insulating stand when a bar magnet is quickly moved along the axis of the coil from one side to the other as shown in the figure alongside.
Answer
Current induced in the coil flows clockwise for an observer sitting on the magnet.
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Question 211 Mark
If the rate of change of current 2 ampere/ second induces an emf of 40 mV in the solenoid, what is the self-inductance of this solenoid?
Answer
Induced emf $\text{e}=-\text{L}\frac{\Delta\text{i}}{\Delta\text{t}}$
$\therefore\text{L}=\frac{\text{e}}{\Big(\frac{\Delta\text{i}}{\Delta\text{t}}\Big)}(\text{numerically})$
$=\frac{40\times10^{-3}}{2}=20\times10^{-3}\text{H}=20\text{mH}$
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Question 221 Mark
Define 1 henry.
Answer
1 henry is self-inductance of that coil in which 1 volt emf is produced when the rate of change of current in that coil is 1A/ s.
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Question 231 Mark
Write SI unit of magnetic flux. Is it a scalar or a vector quantity?
Answer
SI unit of magnetic flux is weber. It is a scalar quantity.
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Question 241 Mark
A bar magnet falls from a height ‘h’ through a metal ring. Will its acceleration be equal to g? Give reason for your answer.
Answer
When magnet falls, the magnetic flux linked through the metal ring changes, so current is induced in the ring which (according to Lenz’s law) opposes the approach of magnet, so its acceleration will be less than g.
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Question 251 Mark
If the self-inductance of an iron core inductor increases from 0·01mH to 10mH on introducing the iron core into it, what is the relative permeability of the core material used?
Answer
Relative permeability $\mu_{\text{r}}=\frac{\text{L}_{\text{medum}}}{\text{L}_{\text{air}}}=\frac{10\text{ mH}}{0.01\text{ mH}}=100$
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Question 261 Mark
Give the direction in which induced current flows in the wire loop, when the magnet moves towards the loop as shown.
Answer
The current induced in the coil will oppose the approach of magnet, so this nearer face of the coil will act as North Pole, therefore on viewing from the magnet side the current in the coil will be anticlockwise.
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Question 271 Mark
A metallic bob A oscillates through the space between the poles of an electromagnet. The oscillations are more quickly damped when the circuit is on, as compared to the case when the circuit is off. Explain.
Answer
When circuit is on the bob will get induced due to magnetic field as it will get attracted towards magnets each time it will move away from its mean position and thus attracted towards mean position. thus its motion is damped more quickly.
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Question 281 Mark
A wheel with 10 metallic spokes each $0.5 m$ long is rotated with a speed of $120 rev / min$ in a plane normal to the horizontal component of earth's magnetic field $H_E$ at a place. If $H_E=0.4 G$ at the place, what is the induced emf between the axle and the rim of the wheel? Note that $1 G =10^{-4} T$.
Answer
$
\begin{aligned}
\text { Induced emf } & =(1 / 2) \omega B R^2 \\
& =(1 / 2) \times 4 \pi \times 0.4 \times 10^{-4} \times(0.5)^2 \\
& =6.28 \times 10^{-5} V
\end{aligned}
$
The number of spokes is immaterial because the emf's across the spokes are in parallel.
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Question 291 Mark
Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a 100 turn coil of area $0.10 m ^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01 T$ perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil?
Answer
Here $v=0.5 Hz ; N=100, A=0.1 m ^2$ and $B=0.01 T$. Employing Eq. (6.19)
$
\begin{aligned}
\varepsilon_0 & =\text { NBA }(2 \pi v) \\
& =100 \times 0.01 \times 0.1 \times 2 \times 3.14 \times 0.5 \\
& =0.314 V
\end{aligned}
$
The maximum voltage is $0.314 V$.
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