Electromagnetic Induction Test

Result

Electromagnetic Induction Test - 72

Score
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Rank
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TIME Taken - -

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Question 1
1 / -0

A thin circular ring of area $$A$$ is held perpendicular to a uniform magnetic field of induction $$B$$. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is $$R$$. When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer

A
$$\dfrac { BR }{ A }$$

B
$$\dfrac { AB }{ R }$$

C
$$ABR$$

D
$$\dfrac { { B }^{ 2 }A }{ { R }^{ 2 } } $$

Solution
Question 2
1 / -0

A thin wire is bent from a square loop $$ABCD$$. A battery of e.m.f. $$2V$$ is connected between the points $$A$$ and $$C$$. The magnetic induction due to the current in the loop at centre $$O$$ will-

A
Be zero

B
Point away from the plane of paper

C
Point along the plane of paper

D
Point into the pane of paper

Solution
Question 3
1 / -0

A small linear segment of an electric circuit is lying on $$x-$$axis extending from $$x=-\dfrac {a}{2}$$ to $$x=\dfrac {a}{2}$$ and a current $$i$$ is following in it. The magnetic induction due to the segment at a point $$x=a$$ will be?

A
$$\propto a$$

B
$$zero$$

C
$$\propto { a }^{ 2 }$$

D
$$\propto \dfrac { 1 }{ a }$$

Solution
Question 4
1 / -0

A uniform with resistance $$20\Omega/m$$ in bent in the form of a circle as shown in the figure. If the equivalent resistance b/w P & Q is 13.8 Omega, then the length of the shown selection is

A
2 m

B
5 m

C
1.8 m

D
18 m

Solution
Question 5
1 / -0

In the figure shown a square loop $$PQRS$$ of side $$'a'$$ and resistance $$'r'$$ is placed in near an infinitely long wire carrying a constant current $$I$$. The sides $$PQ$$ and $$RS$$ are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by $$180^{\circ}$$ about an axis parallel to the long wire and passing through the mid point of the side $$QR$$ and $$PS$$. The total amount of charge which passes through any point of the loop during rotation is

A
$$\dfrac {\mu_{0}Ia}{2\pi} ln2$$

B
$$\dfrac {\mu_{0}Ia}{\pi} ln2$$

C
$$\dfrac {\mu_{0}Ia}{2\pi}$$

D
None of above

Solution
Question 6
1 / -0

A conducting rod of length $$2l$$ is rotating with constant angular speed $$\omega$$ about its perpendicular bisector. A uniform magnetic field $$\vec {B}$$ exists parallel to the axis of rotation. The emf induced between two ends of the rod is

A
$$B\omega l^{2}$$

B
$$\dfrac {1}{2}B\omega l^{2}$$

C
$$\dfrac {1}{8}B\omega l^{2}$$

D
Zero

Solution
Question 7
1 / -0

A conductor having two semicircular section are made to translate in the uniform magnetic filed $$B$$ and $$2B$$ as shown with a constant velocity $$v$$ then the induced emf developed across the ends of conductor is

A
$$6vBR$$

B
$$8vBR$$

C
$$4vBR$$

D
$$2vBR$$

Solution
Question 8
1 / -0

Th circular arc (in $$x-y$$plane) shown in figure rotates (about $$z-axis$$) with a constant angular velocity $$\omega $$. Time in a cycle for which there will be induced $$emf$$ in the loop is:

A
$$\dfrac{\pi}{2\omega }$$

B
$$\dfrac{\pi}{\omega }$$

C
$$\dfrac{2\pi}{3\omega }$$

D
$$\dfrac{3\pi}{2\omega }$$

Solution

Angular velocity=$$\omega$$
$$B.A=\phi, B.A=BA$$
$$emf=\dfrac{d\theta}{dt}$$
$$=BA$$
$$=A\dfrac{dA}{dt}$$
Let $$r$$ be the radius.
$$dA=\dfrac{r^{2}}{2}d\theta$$
$$dE=B.\dfrac{r^{2}}{2}\dfrac{d\theta}{dt}$$
$$\dfrac{Br^2\omega}{2}$$
Time it will be therefore when there is charge in ares.
$$t=\dfrac{\pi}{2\omega}$$
Question 9
1 / -0

A conducting rod of length $$0.5 m $$ rotates about a horizontal axis passing through one of its ends and perpendicular to its length with angular velocity of $$4 rad/s$$. A uniform magnetic field of $$2.0T$$ exists parallel to the axis of rotation. The emf developed across the ends of the conductor will be

A
$$0V$$

B
$$1V$$

C
$$2V$$

D
$$0.5V$$

Solution
Question 10
1 / -0

A metal rod of resistance $$20 \omega$$ is fixed along a diameter of conducting ring of radius 0.1 m and lies in x-y plane. There is a magnetic field $$\overrightarrow B = (50T) \hat{k}.$$ The ring rotates with an angular velocity $$\omega = 20 rad/s$$ about its axis. An external resistance of $$10\Omega$$ is connected across the center of the ring and rim. The current through external resistance is

A
$$\dfrac{1}{4}A$$

B
$$\dfrac{1}{2}A$$

C
$$\dfrac{1}{3}A$$

D
$$zero$$

Solution