An infinite number of charges each equal to q, are placed along X-axis at x = 1, x = 2, x = 4, x = 8, ............... and so on.
(i) Find the electric field at a point x = 0 due to this set up of charges.
(ii) What will be the electric field if in the above set up the consecutive charges have opposite signs.

Show that the force on each plate of a parallel plate capacitor has a magnitude equal to1/2 QE. where Q is the charge on the capacitor and E is the magnitude of electric field between the plates. Explain the origin of the factor 1/2.
Here, we can use the content that the work done in displacing the plates against the force is equal to the increase in energy of the capacitor.

(i) How is the electric field due to a charged parallel plate capacitor affected, when a dielectric slab is inserted between the plates fully occupying the intervening region?
(ii) A slab of material of dielectric constant K has the same area as the plates of a parallel plate capacitor but has thickness \(\frac{1}{2}\) d, where d is the separation between the plates. Find the expression for the capacitance when the slab is inserted between the plates.

An iron sample having mass 8.4 kg is repeatedly taken over cycles of magnetisation and demagnetization at a frequency of 50Hz.It is found that energy of 3.2 J is dissipated as heat in the sample in 30 minutes. If the density of iron is \(7200kg{ m }^{ -3 }\) calculate the value of energy dissipated per unit volume per cycle in the iron sample. 

A 12 V resistance and an inductance of \(\frac { 0.05 }{ \pi } H\)  are connected in series.Across the end of this ciuit an alternating voltage of 130 V and frequency 50 Hz is connected. Calculate the current in the circuit and the potential difference across the inductance.

An electromagnetic wave is travelling in vacum with a speed 3 x 10⁸ m / s. Find its velocity in a medium having relative electric and magnetic permeability 2 and 1, respectively.

(i) Light passes through two polaroids \({ P }_{ 1 }and{ P }_{ 2 }\) with pass axis of \({ P }_{ 2 }\) with pass axis of \({ P }_{ 2 }\) making in angle \(\theta \) with the pass axis of \({ P }_{ 1 }\) . For what value of \(\theta \) is the intensity of emergent light zero?
(ii) A third polaroid is placed between \({ P }_{ 1 }and{ P }_{ 2 }\) with its pass axis making an angle \(\beta \) with the pass axis is \({ P }_{ 1 }\) . Find the value of \(\beta \) for which the intensity of light from \({ P }_{ 2 }\) is \(\frac { { I }_{ 0 } }{ 8 } \) , where \({ I }_{ 0 }\) is the intensity of light on the polaroid \({ P }_{ 1 }\) .

A small metal plate of work function \(\phi \)is kept at a distance r from a singly ionised, fixed ion. A monochromit light beam is incident on the metal plate and photoelectrons are emitted. Find maximum wavelength of the light beam so that some of the electrons may go round the ion along a circle.

An electron, \(\alpha \) -particle and a proton have the same de-Broglie wavelengths. Which of
theseparticle has
(i) minimum kinetic energy?
(ii) maximum kinetic energy and why?
In what way has the wave nature of electron beam exploited in an electron microscope?

A positronium atom is a bound state of an electron \(\left( { e }^{ - } \right) \) and its antiparticle, the positron \(\left( { e }^{ + } \right) \) revolving round their centre of mass. In which part of the em spectrum does the system radiate when it de-excites from its first excited state to the ground state?

(a) Deduce the expression ,N = \({ N }_{ 0 }{ e }^{ -\lambda t }\), for the law of radioactive decay
(b) (i) Write symbolically the process expressing the \({ \beta }^{ + }\) decay of \(_{ 11 }^{ 22 }{ Na }\) . Also write the basic nuclear process underlying this decay.
(ii) Is the nucleus formed in the decay of the nucleus \(_{ 11 }^{ 22 }{ Na }\), an isotope or an isobar?

The diode shown in the figure has a constant voltage drop of 0.5V at all currents and a maximum power rating of 100mW. What should be the value of resistance R connected in series, for maximum current.?

In a silicon transistor, a change of 7.89mA in the emitter current produces a change of 7.8 mA in the collector current. What change in the base current is necessary to produce an equivalent change in the collector current?

Explain that microwaves are better carriers of signals than radio waves?

An audio signal is modulated by a carrier wave of 20 MHz such that the bandwidth required for modulation is 3kHz.Could this wave be demodulated by a diode detector which has the values of R and C as
 (i) R=\(1k\Omega ,C=0.01\mu F\)
 (ii) R=\(10k\Omega ,C=0.01\mu F\)
 (iii) R=\(10k\Omega ,C=1\mu F\)