A conducting square frame of side \(a\) and a long straight wire carrying current \(I\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v.\) The emf induced in the frame will be proportional to:


     
1. \( \frac{1}{x^2} \)
2. \( \frac{1}{(2 x-a)^2} \)
3. \( \frac{1}{(2 x+a)^2} \)
4. \(\frac{1}{(2 x-a)(2 x+a)}\)

Subtopic:  Motional emf |
 72%
From NCERT
NEET - 2015
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A thin semicircular conducting the ring \((PQR)\) of radius \(r\) is falling with its plane vertical in a horizontal magnetic field \(B,\) as shown in the figure. The potential difference developed across the ring when it moves with speed \(v\) is: 

     

1. zero
2. \(Bv\pi r^{2}/2\) and \(P\) is at a higher potential
3. \(\pi rvB\) and \(R\) is at a higher potential
4. \(2BvR\) and \(R\) is at higher potential
Subtopic:  Motional emf |
 74%
From NCERT
AIPMT - 2014
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A coil of self-inductance \(L\) is connected in series with a bulb \(\mathrm{B}\) and an AC source. The brightness of the bulb decreases when:

1. number of turns in the coil is reduced.
2. a capacitance of reactance \(X_C = X_L\) is included in the same circuit.
3. an iron rod is inserted in the coil.
4. frequency of the AC source is decreased.
Subtopic:  Self - Inductance |
 67%
From NCERT
AIPMT - 2013
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A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is:
1. twice per revolution.
2. four times per revolution.
3. six times per revolution.
4. once per revolution.
 
Subtopic:  Faraday's Law & Lenz Law |
 74%
From NCERT
AIPMT - 2013
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A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:
1. \(0.5~\text{A}\)
2. \(0.1~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)

Subtopic:  Faraday's Law & Lenz Law |
 87%
From NCERT
AIPMT - 2012
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The current (\(I\)) in the inductance is varying with time (\(t\)) according to the plot shown in the figure. 

          
Which one of the following is the correct variation of voltage with time in the coil?
1.   2.
3. 4.
Subtopic:  Self - Inductance |
 73%
From NCERT
AIPMT - 2012
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The current \(i\) in a coil varies with time as shown in the figure. The variation of induced emf with time would be:
    

1. 2.
3. 4.
Subtopic:  Faraday's Law & Lenz Law |
 69%
From NCERT
AIPMT - 2011
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A conducting circular loop is placed in a uniform magnetic field, \(B=0.025~\text{T}\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1~\text{mm s}^{-1}\).  The induced emf, when the radius is \(2~\text{cm}\), is:
1. \(2\pi ~\mu\text{V}\)
2. \(\pi ~\mu\text{V}\)
3. \(\frac{\pi}{2}~\mu\text{V}\)
4. \(2 ~\mu \text{V}\)

Subtopic:  Faraday's Law & Lenz Law |
 75%
From NCERT
AIPMT - 2010
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A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of 2 mm/s. The induced e.m.f. in the loop when the radius is 2 cm is:

1. \(3.2\pi ~\mu V\)

2. \(4.8\pi ~\mu V\)

3. \(0.8\pi ~\mu V\)

4. \(1.6\pi ~\mu V\)

Subtopic:  Faraday's Law & Lenz Law |
 69%
From NCERT
AIPMT - 2009
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A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, v=vi^. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops out of the field region, will not remain constant for:

1. the rectangular, circular, and elliptical loops.
2. the circular and the elliptical loops.
3. only the elliptical loop.
4. any of the four loops.

Subtopic:  Motional emf |
 71%
From NCERT
AIPMT - 2009
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