Electromagnetic Induction Test

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Electromagnetic Induction Test - 73

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Question 1
1 / -0

A semicircle loop $$PQ$$ of radius $$'R'$$ is moved with velocity $$'v'$$ in transverse magnetic field as shown in figure. The value of induced emf. between the ends of loop is

A
$$Bv\ (\pi r)$$, end $$'P'$$ at high potential

B
$$2\ BRv$$, end $$P$$ at high potential

C
$$2\ Brv$$, end $$Q$$ at high potential

D
$$B\dfrac {\pi R^{2}}{2}v$$, end $$P$$ at high potential

Solution
Question 2
1 / -0

If number of turns of $$70cm^{2}$$ coil is $$200$$ and it is placed in a magnetic field of $$0.8\ Wb/m^{2}$$ which is perpendicular to the plane of coil and it is rotated through an angle $$180^{\circ}$$ in $$0.1\ sec$$, then induced emf in coil.

A
$$11.2\ V$$

B
$$1.12\ V$$

C
$$224\ V$$

D
$$2.24\ V$$

Solution
Question 3
1 / -0

A rectangular loop is being pulled at a constant speed v, though a region of certian thickness d, in which a uniform magnetic filed B is set up. The graph between position x of the right hand edge of the loop and the induced emf E will be

A

B

C

D

Solution

The question consists of two cases-
Case -1 when the loop entered into the magnetic field
Refer fig,1
let, the breadth of the loop is l then the induced e.m.f is written as-

e.m.f $$=-\dfrac{d\Phi}{dt}=\dfrac{-d}{dt}(BA)$$

$$=-B\dfrac{d(lx)}{dt}$$

e.m.f $$=-Bl\dfrac{dx}{dt}$$

e.m.f $$\propto -\dfrac{dx}{dt}$$

since $$x$$ increases with time t. so

e.m.f $$\propto x$$

case-2 - When the loop leaving the magnetic field

Refer fig, 2

e.m.f $$=\dfrac{-d\Phi}{dt}=\dfrac{-d}{dt}(BA)$$

$$=-B\dfrac{d}{dt}(lx)$$

e.m.f $$=-Bl \dfrac{dx }{dt}$$

e.m.f $$\propto -\dfrac{dx}{dt}$$

since x decreases with time t. so

e.m.f $$\propto -x$$

from above two cases when can draw

Refer fig. 3
Question 4
1 / -0

A conductor PQ with PQ=r, moves with a velocity v in a uniform magnetic filed of induction B. The emf induced in the rod is

A
$$(\underset{v}{\rightarrow} \times\underset{B}{\rightarrow} ).\underset{r}{\rightarrow}$$

B
$$\underset{v}{\rightarrow} . (\underset{r}{\rightarrow} \times\underset{B}{\rightarrow} )$$

C
$$\underset{B}{\rightarrow} . (\underset{r}{\rightarrow} \times\underset{v}{\rightarrow} )$$

D
$$|\underset{r}{\rightarrow} \times (\underset{v}{\rightarrow} \times \underset{B}{\rightarrow} )|$$

Solution
Question 5
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 magnetic induction B constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the filed, as shown in figure. The induced e.m.f is

A
Zero

B
RvB

C
vBl/R

D
vBl

Solution
Question 6
1 / -0

The two rails of railway track, insulated from each other and from the ground, are connected to a mill voltmeter. What will be the reading of the milli voltmeter when a train travels on the track at a speed of $$180 km/hr$$ and earth's magnetic field is $$0.2 \times 10^{-4}T$$ and the rails are separated by 1m.

A
1 m v

B
2 m v

C
3 m v

D
4 m v

Solution
Question 7
1 / -0

A $$50\ Hz$$ $$AC$$ current of crest value $$1\ A$$ flows, through the primary of transformer. If the mutual inductance between the primary and secondary be $$0.5\ H$$, the crest voltage induced in the secondary is

A
175 V

B
150 V

C
100 V

D
157V

Solution
Question 8
1 / -0

A wheel when spokes is rotated in a plane perpendicular to the magnetic filed of earth such that an emf e is induced between axle and rim of the wheel.In the same wheel, number of spokes is made 3 N and the wheel is rotated in the same manner in the same field then new emf is

A
3e

B
$$\dfrac{3}{2}e$$

C
$$\dfrac{e}{3}$$

D
2

Solution
Question 9
1 / -0

The self inductance of a coil having 500 turns is 5 mH. The magnetic flux through the cross - sectional area of the coil while current through it is 8 mA is found to be :

A
$$8\times 10^{-9}Wb$$

B
$$0.8\times 10^{-9}Wb$$

C
$$8\times 10^{-6}Wb$$

D
$$80\times 10^{-3}Wb$$

Solution
Question 10
1 / -0

A square shaped metallic frame $$'PQRS'$$ of dimensions, $$l\times l$$ is placed inside a constant and uniform Magnetic Field $$\vec {B} = B_{0}\left (\dfrac {1}{\sqrt {2}} \hat {i} + \dfrac {1}{\sqrt {2}}\hat {j}\right )$$ as shown in the figure such that it's sides are initially parallel to the $$X$$ and $$Y$$ axes.
In the square loop is now rotated with constant angular speed $$\omega_{0}$$ about an axis parallel to the $$Y - axis$$ and 'bisecting' the area of the loop in the above diagram, the maximum value of the EMF induced (instantaneous) in the loop due to induction will be

A
$$E = B_{0}\omega_{0}l^{2}$$

B
$$E = \dfrac {B_{0}\omega_{0}l^{2}}{\sqrt {2}}$$

C
$$E = \sqrt {2} B_{0}\omega_{0}l^{2}$$

D
$$E = \dfrac {B_{0}\omega_{0}l^{2}}{2}$$