Electromagnetic Induction Test

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Electromagnetic Induction Test - 47

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Question 1
1 / -0

The phenomenon of producing an emf in a circuit whenever the magnetic flux linked with a coil changes is ................................

A
Electro-magnetic induction

B
Inducing current

C
Inducing voltage

D
Change in current

Solution

The phenomenon of producing an emf in a circuit whenever the magnetic flux linked with a coil changes is electromagnetic induction. Electromagnetic induction is the production of an electromotive force (i.e., voltage) across an electrical conductor due to its dynamic interaction with a magnetic field. It has found many applications in technology, including electrical components such as inductors and transformers, and devices such as electric motors and generators.
Question 2
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Which of the following electrical devices works on the principle of electro-magnetic induction ?

A
Electric fan

B
Electric bulb

C
Electric cooker

D
L.E.D.

Solution

Electric fan works on the principle of electro - magnetic induction. An electric fan works with the help of an electric motor the electric motor consists of a coil of wire wound around a metallic core. As electric current passes through the coil of wires, it produces rotational motion due to electro - magnetic induction.
Question 3
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$$A, B$$ and $$C$$ are the three coils of conductor having different number of turns, wound around a soft iron ring as shown in the figure. Ends of coils $$B$$ and $$C$$ are connected to the galvanometers. The observation that can be made when ends of coil $$A$$ are connected to an A.C. source is

A
Same electric current is induced in $$B$$ and $$C$$

B
No electric current is induced in $$B$$ and $$C$$

C
Induced electric current is more in $$B$$ than in $$C$$

D
Induced electric current is less in $$B$$ than in $$C$$

Solution

When the end of coil A is connected to an A.C source the induced electric current will be more in $$B$$ than in $$C$$ as the number of turns in the coil is more in $$B$$ than in $$C$$.
Question 4
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For a current carrying inductor, emf associated in $$20mV$$. Now, current through it changes from $$6A$$ to $$2A$$ in $$2s$$. The coefficient of mutual inductance is

A
$$20mH$$

B
$$10mH$$

C
$$1mH$$

D
$$2mH$$

Solution

$$\displaystyle \left | e \right |=L\frac{dI}{dt}$$
Here, $$\displaystyle e=20mV=20\times 10^{-3}V$$
Coefficient of mutual inductance,
$$ 20\times 10^{-3}=L\times 2$$
$$\displaystyle \therefore L=10\times 10^{-3}=10mH$$
Question 5
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A solenoid $$30 cm$$ long is made by winding $$2000$$ loops of wire on an iron rod whose cross-section is $$1.5{ cm }^{ 2 }$$. If the relative permeability of the iron is $$6000$$. What is the self-inductance of the solenoid?

A
$$15 H$$

B
$$25 H$$

C
$$35 H$$

D
$$5 H$$

Solution

Given : $$\mu_r =6000$$, $$l = 30 cm = 0.3 m$$, $$N = 2000$$
Cross section of solenoid $$A = 1.5 cm^2 = 1.5\times 10^{-4} m^2$$

As we know, Self-inductance of the solenoid
$$L=\dfrac { { \mu }_{ r }\cdot { \mu }_{ 0 }{ N }^{ 2 }A }{ l } $$
$$=\dfrac { 600 0\times 4\pi \times { 10 }^{ -7 }\times { \left( 2000 \right) }^{ 2 }\times \left( 1.5 \right) \times { 10 }^{ -4 } }{ 0.3 } $$
$$=15 H$$
Question 6
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Pick out the wrong statement.

A
Gauss's law of magnetism is given by $$\alpha \phi B. ds = 0$$

B
An EM wave is a wave radiated by a charge at rest and propagates through electric field only

C
A time varying electric field is a source of changing magnetic field

D
Faraday's law of EM induction is $$\phi E. dI = - \dfrac{d \phi_B}{dt}$$

Solution

An electromagnetic wave is the wave radiated by an accelerated charge and propagates through space as coupled electric and magnetic field. These fields are oscillating perpendicular to each other.
Question 7
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Two coils have a mutual inductance $$0.55H$$. The current changes in the first coil according to equation $$I={ I }_{ 0 }\sin { \omega t }$$.
where, $$ { I }_{ 0 }=10A$$ and $$\omega =100\pi { rad }/{ s }$$.
The maximum value of emf in the second coil is

A
$$2\pi $$

B
$$5\pi $$

C
$$\pi $$

D
$$4\pi $$

Solution

E.M.F. $$e=M\dfrac { di }{ dt } =0.005\times \dfrac { d }{ dt } \left( { i }_{ 0 }\sin { \omega t } \right) =0.005\times { i }_{ 0 }\cos { \omega t } $$
$${ e }_{ max }=0.005\times 10\times 100\pi =5\pi $$
Question 8
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The phenomenon of producing an emf in a circuit whenever the magnetic flux linked with a coil changes is ________.

A
Electromagnetic induction

B
Inducing current

C
Inducing voltage

D
Change in current

Solution

Electromagnetic induction is the phenomenon of producing an emf in a circuit whenever there is a change in magnetic flux linked with the coil. Lenz's law states that if the magnetic flux linked with the coil changes, an emf is induced in the coil in such a way so as to oppose that change in magnetic flux.
Question 9
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In the figure shown, the magnetic field induction as the point $$O$$ will be

A
$$\dfrac { { \mu }_{ 0 }i }{ 2\pi r } $$

B
$$\left( \dfrac { { \mu }_{ 0 } }{ 4\pi } \right) \left( \dfrac { i }{ r } \right) \left( \pi +2 \right) $$

C
$$\left( \dfrac { { \mu }_{ 0 } }{ 4\pi } \right) \left( \dfrac { i }{ r } \right) \left( \pi +1 \right) $$

D
$$\dfrac { { \mu }_{ 0 }i }{ 4\pi r } \left( \pi -2 \right) $$

Solution

Field due to a straight wire of infinite length is $$\dfrac { { \mu }_{ 0 }i }{ 4\pi r }$$ if the point is on a line perpendicular to its length while at the centre of a semicircular coil is $$ \dfrac { { \mu }_{ 0 }\pi i }{ 4\pi r } $$
$$\therefore B={ B }_{ a }+{ B }_{ b }+{ B }_{ c }$$
$$=\dfrac { { \mu }_{ 0 } }{ 4\pi } \dfrac { i }{ r } +\dfrac { { \mu }_{ 0 } }{ 4\pi } \dfrac { \pi i }{ r } +\dfrac { { \mu }_{ 0 } }{ 4\pi } \dfrac { i }{ r }$$
$$ =\dfrac { { \mu }_{ 0 }i }{ 4\pi r } \left( \pi +2 \right) $$ out of the phase
Question 10
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Two Circular cells can be arranged in any of the three following situations as shown in figure. Their mutual inductance will be Maximum in which arrangement ?

A
(A)

B
(B)

C
(C)

D
Same in all conditions

Solution

The mutual inductance between two coils depends on their degree of flux linkage i.e. the fraction of flux linked with one coil which is also linked to the other coil.
Here, the two coils in arrangement (A) are placed with their planes parallel which allows maximum flux.