Electromagnetic Induction Test

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Electromagnetic Induction Test - 58

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Question 1
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A wire of fixed length is wound on a solenoid of length l and radius r. Its self inductance is found to be L. Now, if same wire is wound on a solenoid of length $$\dfrac{l}{2}$$ and radius $$\dfrac{r}{2}$$, then self inductance will be

A
2L

B
$$\dfrac{L}{2}$$

C
3L

D
4L

Solution

$$L=\mu _{0}\times n^{2}\times V$$ (n $$\rightarrow $$ Number of turns per unit length , V $$\rightarrow $$ Volume of cylinder)
$$=\mu _{0}\times \frac{N^{2}}{l^{2}}\times \pi r^{2}\times l$$
$$L=\frac{\mu _{0}N^{2}\pi r^{2}}{l}$$
Let length of wire be $$l_{1}$$
$$l_{1}=(2\pi r)\times N \Rightarrow N=(\frac{l_{1}}{2\pi r})$$
$$L=\frac{\mu _{0}\pi r^{2}}{l}\times \frac{l_{1}^{2}}{4\pi ^{2}r^{2}}=\frac{\mu _{0}l_{1}^{2}}{4\pi l}$$
$$\therefore L \propto \frac{1}{l}\Rightarrow \frac{L_{2}}{L_{1}}=\frac{l_{1}}{l_{2}}=\frac{l}{\frac{l}{2}}=2$$
$$L_{2}=2L_{1}$$
Question 2
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Electro motive force induced by motion of conductor across magnetic field is called

A
EMF

B
motional EMF

C
static EMF

D
rotational EMF

Solution
Question 3
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A cylindrical magnet is kept along the axis of a circular coil. On rotating the magnet about its axis. the coil will have induced in it

A
No current

B
A current

C
Only an e.m.f.

D
Both an e.m.f. and a current

Solution

No, Current will not be induced in the coil if the coil is rotated about it's axis
Formula for the flux is. $$\phi$$ = NBA = constant
$$\therefore$$ i = $$\frac{d\phi}{dt}$$ = 0
i = 0
Question 4
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Magnetic flux in the circuit containing a coil of resistance 2 ohm changes from 2.0 wb to 10 wb in 0.2 sec. the charge passed through the coil in this time is

A
0.8 C

B
1.0 C

C
5.0C

D
4.0C
Question 5
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A magnetic field of flux density $$10 T$$ acts normal to a coil of $$50$$ turns having $$100$$ $$cm^2$$ area. The e.m.f. induced if the coil is removed from the magnetic field in $$0.1$$ seconds is:

A
$$50 V$$

B
$$60 V$$

C
$$80 V$$

D
$$40 V$$

Solution

In this case, $$B=10T\, ,N=50\,turns\, ,A=100\,cm^2=10^{-2}m^2$$ and $$dt=0.1\,s$$

We know that,

$$\phi_1=NBA\,Cos\,\theta=NBA$$ (as $$Cos\theta=Cos0=1$$)

Therefore,

$$\phi_1=50\times 10\times 10^{-2}=5\,weber$$

When the coil is removed from the magnetic field, $$B=0$$

So,

$$\phi_2=0$$

Therefore,

$$\phi_1-\phi_2=d\phi=0-5=-5\,weber$$.

We also know that $$e=-\dfrac{d\phi}{dt}=\dfrac{-5}{0.1}=50\,V$$

Hence, the induced emf if the coil is removed from the magnetic field in $$0.1$$ second is $$50\,V$$.
Question 6
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A constant current $$I_{0}$$ is passing through a long straight wire (shown in figure).
A rectangular loop of total resistance $$R$$ is moving parallel to the wire. Then:

A
the heat generated in the loop is with constant rate.

B
current in the loop is zero

C
velocity of loop decreases according to Lenz's law

D
none of the above

Solution

The magnetic flux in the loop remains constant induced emf in the loop is zero.
Hence, induced current in loop is zero.
Question 7
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When current changes from $$13\ A$$ to $$7\ A$$ in $$0.5\ sec$$ through a coil, the emf induced is $$3\times 10^{-4}\ V$$. The coefficient of self induction is:

A
$$25\times 10^{-3}\ H$$

B
$$25\times 10^{-4}\ H$$

C
$$25\times 10^{-5}\ H$$

D
$$25\times 10^{-6}\ H$$

Solution
Question 8
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The magnetic flux $$\phi$$ (in weber) in a closed circuit of resistance $$10\ ohm$$ varies with time $$t$$ (in second) according to equation $$\phi=6t^{2}-5t+1$$. The magnitude of induced current at $$t=0.25\ s$$ is:

A
$$1.2\ A$$

B
$$0.8\ A$$

C
$$0.6\ A$$

D
$$0.2\ A$$

Solution
Question 9
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Self inductance of coil measures

A
electrical inertia

B
electrical friction

C
induced emf

D
induced current

Solution
Question 10
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Which type of current can be obtained from an electric generator?

A
Only DC

B
Only AC

C
Both AC and DC at a time

D
It is dependent on the type of an electric generator.

Solution