\(Here,r=10cm={ 10 }^{ -1 }m,\omega =20\pi rad/s\)
\(B=0.2T,e=?\)
Potential difference developed between the axis of the disc and its rim, \(e=\frac { 1 }{ 2 } B{ r }^{ 2 }\omega \)
\( e=\frac { 1 }{ 2 } \times 0.2{ { (10 }^{ -1 }) }^{ 2 } \times 20\pi =0.0629V\)
\(Induced\ current,\ i=\frac { e }{ R } =\frac { 0.0628 }{ 2 } =0.0314A\)

\(e=?; \ n=200; \ A=0.16{ m }^{ 2 };\)
\({ B }_{ 1 }=0.10 \ Wb{ m }^{ -2 };\ { B }_{ 2 }=0.30\ Wb{ m }^{ -2 }\)
\({ \phi }_{ 2 }-{ \phi }_{ 1 }=NA\left( { B }_{ 2 }-{ B }_{ 1 } \right) =200\times 0.16\left( 0.30-0.10 \right) \)
\({ \phi }_{ 2 }-{ \phi }_{ 1 }=6.4Wb\)
\(dt=0.05s\)
\(e=\frac { d\phi }{ dt } =\frac { { \phi }_{ 2 }-{ \phi }_{ 1 } }{ dt } \ \left[ in\ magnitude \right] \)
\(e=\frac { 6.4 }{ 0.05 } =\frac { 640 }{ 5 } or\ e=128V\)     

emf induced
e = Blv
= 0.1 x 10 x 10^-2 x 20 V
= 0.2 volt
(ii) Current in the loop
\(i=\frac{e}{R} \) 
\(=\frac{0.2}{2}A=0.1A\)

When a bulk piece of the conductor is subjected to a changing magnitude flux, the induced current, developed in a spiral form is called eddy current
Any two uses:
1. Magnetic brakes in trains
2. Electromagnetic damping
3. Induction furnaces
4. Electric power meter
5. Induction therapy
6. To find the melting point of precious metals 
7. In speedometer of vehicles

Deplection region is a region created around the \(p-n\) junction which is devoid of free charge carriers and has immobile ions. It is created due to diffusion of majority carriers across the junction when \(p-n\) junction is formed.
Potential barrier is a potential difference or junction voltage developed across the junction due to migration of majority carriers across the \(p-n\) junction due to this junction voltage, it appears as if a fictitious battery is connected across the \(p-n\) junction, with its positive terminal to \(n\)-region and negative terminal to \(p\)-region of  \(p-n\) junction. The value of potential barrier is 0.3 volt for germanium and 0.7 volt for silicon semiconductor diode.

(a) Due to the diffusion of electrons and the holes, from their majority zone to minority zone, a layer of positive and negative space charge region on either side on the junction is formed. This is called the depletion region.
The loss of electrons, from n-region and gain of electrons by the p-region, causes a difference of potential across the junction. This tends to prevent the movement of charge carriers across the junction and is, therefore, termed as barrier potential.

For positive half cycle of input ac, one of the two diodes gets forward biased and conducts and output current is obtained across the load RL, For negative half cycle of input ac, the other diode
gets forward biased and thus output current is obtained due to it. Therefore, output is obtained for both the cycles of input ac.

(a) It works on the principle of electromagnetic induction, i.e. when a coil continuously rotates in a magnetic field, the magnetic flux associated with it keeps on changing; thus an emf is induced in it.
(b) When the coil rotates in a magnetic field, its effective area i.e. A cos S, (i.e. area normal to the magnetic field) keeps on changing. Hence magnetic flux NBA cos S, keeps on changing.
(c) Let the coil be rotating with angular velocity 'm', at any instant 't' when the normal to the plane of the coil makes an angle t with the magnetic field. Hence magnetic flux,
\(\emptyset=NBA\cos\omega,\)therefore induced emf \((\epsilon)\)
\(\epsilon=-\frac{{d}\epsilon}{{dt}}\)
\(\Rightarrow \epsilon =NBA\omega \sin { \omega t } \)
Induced emf will be maximum when \(\omega{t}=90^{\circ }\)
Hence,\(\epsilon_{max}=NBA\omega\)
The direction of induced emf can be determined using Fleming's right hand rule. Alternatively, Statement of the above rule.
(d)