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:

$\mathrm{}$
$\mathrm{}$
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. \(+ Blv  ~\text{for}  ~ b \leq x < 2 b , ~~~  0  ~\text{for}~   0 \leq x < b\)
$$

$\mathrm{}$

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:

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

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. \(\dfrac{{B}^2 {l}^2 {v}}{2{r}}~~\text{for}~0 \leq {x}<{b},~~~ 0~~\text{for} ~{b} \leq {x}<2 {b}\)

2. \(\dfrac{{B}^2 {l}^2 {v^2}}{{r}}~~\text{for}~0 \leq {x}<{b},~~~ 0~~\text{for} ~{b} \leq {x}<2 {b}\)

3. \(0~~\text{for}~b \leq {x}<{2b},~~~ \dfrac{{B}^2 {l}^2 {v}^2}{{r}}~~\text{for} ~{0} \leq {x}< {b}\)

4. \(0~~\text{for}~b \leq {x}<{2b},~~~ \dfrac{{B}^2 {l}^2 {v}}{{2r}}~~\text{for} ~{0} \leq {x}< {b}\)

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

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:

The ratio of magnetic energy per unit volume and electrostatic energy stored per unit volume in a parallel plate capacitor is:
1. \(\left(\dfrac{1}{\varepsilon_0 \mu_0}\right)\dfrac{B^2}{E}\)

2. \(\left(\dfrac{1}{\varepsilon_0 \mu_0}\right)\dfrac{E^2}{B}\)

3. \(\left(\dfrac{1}{2\varepsilon_0 \mu_0}\right)\dfrac{B^2}{E}\)

4. \(\left(\dfrac{1}{2\varepsilon_0 \mu_0}\right)\dfrac{E^2}{B}\)$\mathrm{}$

Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a \(100\) turn coil of an area of \(0.10~\text{m}^2\). The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of \(0.01~\text{T}\) perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil?
1. \(0.628~\text{V}\)
2. \(0.421~\text{V}\)
3. \(0.314~\text{V}\)
4. \(0\) 

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. \(133 ~\text V\)

The polarity of the capacitor in the given figure is: