# A circular loop of radius R carrying current i lies in the x-y plane. If the centre of the loop coincides with the origin, then the total magnetic flux passing through the x-y plane will be: 1.  directly proportional to I. 2.  directly proportional to R. 3.  directly proportional to R2. 4.  Zero.

Subtopic:  Magnetic Flux |
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A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region:

1. is zero
2. decreases as $\frac{1}{r}$
3. increases as r
4. decreases as $\frac{1}{{r}^{2}}$

Subtopic:  Faraday's Law & Lenz Law |
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Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:

 1 maximum in the situation (A). 2 maximum in the situation (B). 3 maximum in the situation (C). 4 the same in all situations.

Subtopic:  Mutual Inductance |
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A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\stackrel{\to }{B}$ exists parallel to the axis of rotation. The e.m.f. induced between the two ends of the rod is:

1. $$B\omega l^2$$
2. $\frac{1}{2}B\omega {l}^{2}$
3. $\frac{1}{8}B\omega {l}^{2}$
4. Zero

Subtopic:  Motional emf |
60%
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A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of $$1~\mathrm{wb/m^2}$$, as shown in fig. If all the four sides are of 1 m length each, then the induced emf between points A and D is:

1. 0

2. 1.41 volt

3. 0.71 volt

4. None of the above

Subtopic:  Motional emf |
73%
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A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of:

 1 $${mgR \over Bl}$$ 2 $${mgR \over B^2l^2}$$ 3 $${mgR \over B^3l^3}$$ 4 $${mgR \over B^2l}$$
Subtopic:  Motional emf |
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A conducting rod AC of length 4l is rotated about point O in a uniform magnetic field $\stackrel{\to }{B}$ directed into the paper. If AO = l and OC = 3l, then:

1. ${V}_{A}-{V}_{O}=\frac{B\omega {l}^{2}}{2}$
2. ${V}_{O}-{V}_{C}=\frac{7}{2}B\omega {l}^{2}$
3. ${V}_{A}-{V}_{C}=4B\omega {l}^{2}$
4. ${V}_{C}-{V}_{O}=\frac{9}{2}B\omega {l}^{2}$

Subtopic:  Motional emf |
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The graph gives the magnitude $$B(t)$$ of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first:

 1 $$b > (d = e) < (a = c)$$ 2 $$b > (d = e) > (a = c)$$ 3 $$b < d < e < c < a$$ 4 $$b > (a = c) > (d = e)$$

Subtopic:  Faraday's Law & Lenz Law |
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A square loop of side 5 cm enters a magnetic field with 1 cms-1. If the front edge enters the magnetic field at t = 0, then which graph best depicts emf?

 1 2 3 4

Subtopic:  Motional emf |
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A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity $\mathrm{\omega }$. The maximum value of the emf induced in it is:

1. $\frac{\mathrm{NBA}}{\mathrm{\omega }}$

2. $\mathrm{NBA\omega }$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega }}^{2}}$

4. ${\mathrm{NBA\omega }}^{2}$

Subtopic:  Faraday's Law & Lenz Law |
88%
From NCERT
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