# In a coil of resistance $$10$$ $$\Omega$$, the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:       1. $$2$$ 2. $$6$$ 3. $$4$$ 4. $$8$$

Subtopic: Â Magnetic Flux |
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The figure shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normally to the plane of the loop away from the reader. Then:

 1 for the rectangular loop abcd, the induced current is clockwise. 2 for the triangular loop abc, the induced current is clockwise. 3 for the irregularly shaped loop abcd, the induced current is anti-clockwise. 4 none of these.

Subtopic: Â Faraday's Law & Lenz Law |
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A wheel with $$10$$ metallic spokes each $$0.5$$ m long is rotated with a speed of $$120$$ rev/min in a plane normal to the horizontal component of earth’s magnetic field HE at a place. If $$H_E=0.4$$ G at the place, what is the induced emf between the axle and the rim of the wheel? ($$1$$ G=$$10^{-4}$$ T)
1. $$5.12\times10^{-5}$$ T
2. $$0$$
3. $$3.33\times10^{-5}$$
4. $$6.28\times10^{-5}$$

Subtopic: Â Motional emf |
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Two concentric circular coils, one of small radius $${r_1}$$ and the other of large radius $${r_2},$$ such that $${r_1<<r_2},$$  are placed co-axially with centres coinciding. The mutual inductance of the arrangement is:
1. $$\dfrac{\mu_0\pi r_1^2}{3r_2}$$

2. $$\dfrac{2\mu_0\pi r_1^2}{r_2}$$
3. $$\dfrac{\mu_0\pi r_1^2}{r_2}$$
4. $$\dfrac{\mu_0\pi r_1^2}{2r_2}$$

Subtopic: Â Mutual Inductance |
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The expression for the magnetic energy stored in a solenoid in terms of magnetic field $$B$$, area $$A$$ and length $$l$$ of the solenoid is:

 1 $$\dfrac{1}{\mu_0}B^2Al$$ 2 $$\dfrac{1}{2\mu_0}B^2Al$$ 3 $$\dfrac{2}{\mu_0}B^2Al$$ 4 $$\dfrac{3}{2\mu_0}B^2Al$$
Subtopic: Â Self - Inductance |
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A rod of length $$l$$ rotates with a uniform angular velocity $$\omega$$ about its perpendicular bisector. A uniform magnetic field $$B$$ exists parallel to the axis of rotation. The potential difference between the two ends of the rod is:
1. zero
2. $$\frac{1}{2}Bl\omega ^{2}$$
3. $$Bl\omega ^{2}$$
4. $$2Bl\omega ^{2}$$

Subtopic: Â Motional emf |
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A conducting rod is moved with a constant velocity $$v$$ in a magnetic field. A potential difference appears across the two ends,

 a. if $$\overrightarrow v \|\overrightarrow l$$ b. if  $$\overrightarrow v \|\overrightarrow B$$ c. if  $$\overrightarrow l \|\overrightarrow B$$ d. none of these

Choose the correct option:

 1 (a), (b) 2 (b), (c) 3 (d) only 4 (a), (d)

Subtopic: Â Motional emf |
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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 |
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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 |
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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 |
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