# A square wire loop of resistance $$0.5$$ $$\Omega$$/m, having a side $$10$$ cm and made of $$100$$ turns is suddenly flipped in a magnetic field $$B,$$ which is perpendicular to the plane of the loop. A charge of $$2\times10^{-4}$$ C passes through the loop. The magnetic field $$B$$ has the magnitude of:  1. $$2\times10^{-6}$$ T 2. $$4\times10^{-6}$$ T 3. $$2\times10^{-3}$$ T 4. $$4\times10^{-3}$$ T

Subtopic: Â Magnetic Flux |
From NCERT
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A rectangular loop of conducting wire is bent symmetrically so that its two plane halves are inclined at right angles with respect to each other (i.e. $$\angle \text { PQR }=\angle S T U=90^{\circ}$$). Every segment has a length 'a' (PQ = QR = RS = ... = UP = a). A uniform time-dependent magnetic field B(t) acts on the loop, making an angle '$$\alpha$$' with the lower half of the loop and '$$90^o - \alpha$$' with the upper half. The EMF induced in the loop is proportional to:

$$1.~ (\cos \alpha+\sin \alpha) \frac{d B}{d t}\\ 2.~ (\cos \alpha-\sin \alpha) \frac{d B}{d t}\\ 3.~ (\tan \alpha+\cot \alpha) \frac{d B}{d t}\\ 4.~ (\tan \alpha-\cot \alpha) \frac{dB}{d t}$$
Subtopic: Â Faraday's Law & Lenz Law |
From NCERT
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A circular loop of radius $$\mathrm{R}$$, enters a region of uniform magnetic field $$\mathrm{B}$$ as shown in the diagram. The field $$(\mathrm{B})$$ is perpendicular to the plane of the loop while the velocity of the loop,$$\mathrm{v}$$, is along its plane. The induced EMF:

 1 increases continuously. 2 decreases continuously. 3 first increases and then decreases. 4 remains constant throughout.
Subtopic: Â Faraday's Law & Lenz Law |
Â 69%
From NCERT
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A triangular wire frame, in the form of an equilateral triangle PQR moves with a uniform velocity into a region where there is a uniform magnetic field $$B$$. The edge PQ is parallel to the boundary of the region and the velocity $$v$$ is perpendicular to it. The emf($$E$$) induced within the frame is plotted as a function of time $$t,$$ starting from when the frame enters the magnetic field. $$E$$ is given by:

1. $$Bv^2t$$
2. $$2Bv^2t$$
3. $$\frac{\sqrt3}{2}Bv^2t$$
4. $$\frac{2}{\sqrt3}Bv^2t$$
Subtopic: Â Motional emf |
From NCERT
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A small solenoid is kept inside a much larger solenoid, with their axes parallel to each other. The small solenoid has a cross-sectional radius $$r_1,$$ length $$l_1$$ and the total number of turns $$N_1.$$ The corresponding quantities for the larger solenoid are: $$r_2,~ l_2,~ N_2$$ respectively.
Their mutual inductance is (nearly) given by:
1. $$\frac{\mu_0\pi r^2_1N_1N_2}{l_2}$$
2. $$\frac{\mu_0\pi r^2_1N_1N_2}{\sqrt{l_1l_2}}$$
3. $$\frac{\mu_0\pi r^2_1N_1N_2}{l_1}$$
4. $$\frac{\mu_0~\pi r_1r_2N_1N_2}{\sqrt{l_1}}$$
Subtopic: Â Mutual Inductance |
Â 62%
From NCERT
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A rod $$\mathrm{XY}$$ of length $$l$$ is placed in a uniform magnetic field $$B$$, as shown in the diagram. The rod moves with a velocity $$v$$, making an angle of $$60^\circ$$ with its length. The emf induced in the rod is:
 1 $$vBl$$ 2 $$vBl \over 2$$ 3 $${\sqrt 3 \over 2}vBl$$ 4 $${1 \over \sqrt 3}vBl$$
Subtopic: Â Motional emf |
Â 72%
From NCERT
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A straight horizontal wire of mass $$m$$ and length $$l,$$ and having a negligible resistance can slide freely on a pair of conducting parallel rails, placed vertically. The rails are connected at the top by a capacitor $$C.$$ A uniform magnetic field $$B$$ exists in the region, perpendicular to the plane of the rails. The wire:

 1 falls with uniform velocity. 2 accelerates down with acceleration less than $$g$$. 3 accelerates down with acceleration equal to  $$g$$. 4 moves down and eventually comes to rest.
Subtopic: Â Motional emf |
Â 70%
From NCERT
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The self-inductance of a long solenoid of cross-section $$A,$$ total length $$L$$ and total number of turns $$N,$$ is (approximately):
 1 $$\dfrac{\mu_0A}{L}\cdot N$$ 2 $$\dfrac{\mu_0A}{L}\cdot N^2$$ 3 $$\dfrac{\mu_0L^3}{A}\cdot N$$ 4 $$\dfrac{\mu_0L^3}{A}\cdot N^2$$
Subtopic: Â Self - Inductance |
Â 79%
From NCERT
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A conducting circular wire of radius $$r$$ is moving with constant velocity $$v$$ towards the right in a uniform magnetic field $$B.$$ We consider two points $$X,Y$$ such that chord $$XY$$ is perpendicular to the velocity $$v$$ and is at a distance $$x$$ from the centre $$(O)$$ of the circle. The EMF induced between $$X,Y$$ is $$\varepsilon.$$ Then, $$\varepsilon$$ is proportional to:

1. $$x$$
2. $$\sqrt{r^2-x^2}$$
3. $$r$$
4. $$x\sqrt{r^2-x^2}$$
Subtopic: Â Motional emf |
Â 73%
From NCERT
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An $$L$$-shaped rod $$(ABC;AB=BC=a)$$ moves in its own plane with a velocity $$v$$ parallel to $$AB.$$ There is a uniform magnetic field $$B$$ acting into the plane as shown. The emf developed between $$A,C$$ is:

1. $$Bav$$
2. $$\sqrt2Bav$$
3. $$\frac{Bav}{2}$$
4. zero
Subtopic: Â Motional emf |
Â 55%
From NCERT