A square loop of side \(10~\text{cm}\) and resistance \(0.5~\Omega\)$$ is placed vertically in the east-west plane. A uniform magnetic field of \(0.10~\text{T}\) is set up across the plane in the north-east direction. The magnetic field is decreased to zero in \(0.70~\text{s}\) at a steady rate. The magnitude of induced current during this time interval is:
1. \(2~\text{mA}\)
2. \(1~\text{mA}\)
3. \(0.5~\text{mA}\)
4. \(3~\text{mA}\)

A circular coil of radius \(10~\text{cm}\), \(500\) turns, and resistance \(2~\Omega\)$$ is placed with its plane perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through \(180^{\circ}\) in \(0.25~\text{s}\). The magnitude of the current induced in the coil is:
(The horizontal component of the earth’s magnetic field at the place is \(3.0\times10^{-5}~\text{T}\))
1. \(3~\text{mA}\)
2. \(2.25~\text{mA}\)
3. \(5.2~\text{mA}\)
4. \(1.9~\text{mA}\)

Consider the figure. What would you do to obtain a large deflection of the galvanometer?    

1. Use a rod made of soft iron inside the coil $C_2$

2. Connect the coil to a powerful battery

3. Move the arrangement rapidly towards the test coil $C_1$.

4. All of the above

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:

Mark the correct statement:

A rectangular loop and a circular loop are moving out of a uniform magnetic field region (as shown in the figure) to a field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops.

1. Only in the case of the rectangular loop

2. Only in the case of the circular loop

3. In both cases

4. None of these

The polarity of the capacitor in the given figure is:

A metallic rod of \(1 ~\text m\) length is rotated with a frequency of \(50 ~\text{rev/s},\) with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius \(1 ~\text m,\) about an axis passing through the centre and perpendicular to the plane of the ring (as shown in the figure). A constant and uniform magnetic field of \(1 ~\text T\) parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?

   
1. \(150 ~\text V\)
2. \(130 ~\text V\)
3. \(157 ~\text V\)
4. \(133 ~\text V\)

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 H_E 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. \(6.28\times10^{-5}\)

Refer to figure. The arm \(PQ\) of the rectangular conductor is moved from \(x = 0,\) outwards. The uniform magnetic field is perpendicular to the plane and extends from \(x = 0\) to \(x = b\) and is zero for \(x > b.\) Only the arm \(PQ\) possesses substantial resistance \(r.\) Consider the situation when the arm \(PQ\) is pulled outwards from \(x = 0\) to \(x = 2b\) with a` constant speed \(v.\) The induced emf is:

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1. \(- Blv   ~\text{for }~  0 \leq x < b ,~~~   0   ~\text{for}~   b \leq x < 2 b\)
2. \(  + Blv   ~\text{for}~   0 \leq x < b ,   ~~~0   ~\text{for }~  b \leq x < 2 b\)
3. \(- Blv   ~\text{for}~   b \leq x < 2 b ,  ~~~0 ~\text{for }~  0 \leq x < b\)
4. \(+ Blv  ~\text{for}  ~ b \leq x < 2 b , ~~~  0  ~\text{for}~   0 \leq x < b\)
$$

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