Electromagnetic Induction Test

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Electromagnetic Induction Test - 59

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Question 1
1 / -0

The magnetic flux linked with a coil varies as $$\phi =3t^2+4t+9$$. The magnitude of the emf induced at $$t=2$$ seconds is?

A
$$8$$ V

B
$$16$$ V

C
$$32$$ V

D
$$64$$ V

Solution

$$\phi =\dfrac{d\theta}{dt}$$
$$=6t+4=6(2)+4$$
$$=16V$$.
Question 2
1 / -0

The current carrying wire and the rod AB are in same plane. The rod moves parallel to the wire with a velocity v. Which on of the following statement is true about induced emf in the rod?

A
End A will be at lower potential with respect to B

B
A and B will be at same potential

C
There will be no induced emf in the rod.

D
Potential at A be higher than that at B

Solution
Question 3
1 / -0

Two coils have a mutual inductance of $$0.01H$$. The current in the first coil changes according to equation $$I=5\sin 200\pi t$$. The maximum value of e.m.f. induced in the second coil is?

A
$$10\pi$$ volt

B
$$0.1\pi$$ volt

C
$$\pi$$ volt

D
$$0.01\pi$$ volt

Solution

E.M.F induced $$(e) = M \dfrac{di}{dt}$$

$$ = M \dfrac{d}{dt} (i_{0} \sin \omega t)$$

$$ = M i_{0} \omega \cos \omega t$$

Given: $$M = 0.01H; I = 5 \sin 200 \pi t$$

$$ \Rightarrow\ i_{0} = 5$$

$$\omega = 200 \pi $$

$$\therefore $$ Maximum value of emf induced $$(e_{\text{max}})$$
$$ = M i_{0} \omega$$

$$ = 0.01 \times 5 \times 200 \pi $$

$$\therefore$$ $$\boxed{e_{\text{max}} = 10 \pi\ \text{Volt}} $$
Question 4
1 / -0

A non-conducting ring of radius $$r$$ has charge per unit length $$\lambda$$. A magnetic field perpendicular to plane of the ring changes at rate $$dB/dt$$. Torque experienced by the ring is :

A
$$\lambda \pi r^3\dfrac{dB}{dt}$$

B
$$\lambda 2\pi r^3\dfrac{dB}{dt}$$

C
$$\lambda ^2 (2\pi r)^2r \dfrac{dB}{dt}$$

D
$$zero$$

Solution
Question 5
1 / -0

Consider the following statements:
(A) an emf can be induced by moving a conductor in a magnetic field
(B) An emf can be induced by changing the magnetic field

A
Both $$A$$ and $$B$$ are true

B
$$A$$ is true but $$B$$ is false

C
$$B$$ is true but $$A$$ is false

D
Both $$A$$ and $$B$$ are false

Solution
Question 6
1 / -0

A conducting square loop of side $$l$$ and resistance $$R$$ moves in its plane with a uniform velocity $$v$$ perpendicular to one of its sides. A uniform and constant magnetic field $$B$$ exists along the perpendicular to the plane of the loop as shown in figure. The current induced in the loop is

A
$$Blv/R$$ clockwise

B
$$Blv/R$$ anticlockwise

C
$$2Blv/R$$ anticlockwise

D
zero

Solution
Question 7
1 / -0

A small circular loop of radius $$r$$ is placed inside a circular loop of radius $$R(R>>r)$$. The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to :

A
$$r/R$$

B
$$r^2/R$$

C
$$r/R^2$$

D
$$r^2/R^2$$

Solution
Question 8
1 / -0

Consider the situation shown in figure. The wire $$AB$$ is slid on the fixed rails with a constant velocity. If the wire $$AB$$ is replaced by a semicircular wire, the magnitude of the induced current will

A
increase

B
remain the same

C
decreases

D
increase or decrease depending on whether the semi-circle bulges towards the resistance or away from it

Solution
Question 9
1 / -0

The inductance of a coil in which a current of $$0.1\ A$$ increasing at the rate of $$0.5\ A/s$$ represents a power flow of $$\dfrac{1}{2}\ watt$$, is :

A
$$2\ H$$

B
$$8\ H$$

C
$$20\ H$$

D
$$10\ H$$

Solution
Question 10
1 / -0

A square conducting loop, 20.0 cm on a side is placed in the same magnetic field as shown in Fig. Centre of the magnetic field region, where $$db/dt =0.035 T s^{-1}$$

The current induced in the loop if its resistance is $$2.00 \Omega$$ is

A
$$2.50 \times 10^{-4}A$$

B
$$4.35 \times 10^{-4}A$$

C
$$1.25 \times 10^{-4}A$$

D
$$7.37 \times 10^{-4}A$$

Solution

As we know that
$$I=\dfrac {\epsilon}{R}=\dfrac {A}{R} $$

$$\dfrac {dB}{dt}=\dfrac {L^2}{R}dfrac {dB}{dt}$$

$$= \dfrac {(0.20 m)^2 (0.0350 T/s)}{1.90 \omega}$$

$$7.37 \times 10^{-4}A$$