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.

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 m length is rotated with a frequency of 50 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 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 T parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?

1. 150 V

2. 130 V

3. 157 V

4. 133V

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:

$1. -\mathrm{Blv} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$2. +\mathrm{Blv} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$3. -\mathrm{Blv} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b}$
$4. +\mathrm{Blv} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b}$

Refer to the 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 constant speed v. The force necessary to pull the arm is:

$1. \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$2. \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{2\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$3. 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{\mathrm{r}} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$4. 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{2\mathrm{r}} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$

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 and is then moved back to x = 0 with constant speed v. The power dissipated as Joule heat is: 

$1. \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{2\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$2. \frac{{\mathrm{B}}^2{\mathrm{l}}^2{\mathrm{v}}^2}{\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}$
$3. 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2{\mathrm{v}}^2}{\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}$
$4. 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2{\mathrm{v}}^2}{2\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}$

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. \(\frac{\mu_0\pi r_1^2}{3r_2}\)
2. \(\frac{2\mu_0\pi r_1^2}{r_2}\)
3. \(\frac{\mu_0\pi r_1^2}{r_2}\)
4. \(\frac{\mu_0\pi r_1^2}{2r_2}\)