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.

A long horizontal rigidly supported wire carries \({ i }_{ a }\)of 100 A. Directed above it and parallels to it is a fine wire that carries a current \({ i }_{ a }\)of 20A and weighs 0.073N/m. How far above the lower wire should the second wire be kept if we wish to support it by magnetic repulsion?
Given permeability constant \({ \mu }_{ 0 }=4\pi \times { 10 }^{ -7 } \ Wb\ { A }^{ -1 }{ m }^{ -1 }\)

When a capacitor is connected in series LR circuit the alternating current flowing in the circuit increases. Explain why.

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 \({ P }_{ 1 }\) .

The fringe width in a young's doubt slit experiment is mm, distance between slit and screen is 1.2m and separation between the slits is 0.24mm. The radiation of same source is incident on a photo-cathode of work function 2.2 eV. Find the stopping potential.

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?

Consider a radioactive nucleus A which decays to a stable nucleus C through the following sequence:
  A \(\longrightarrow \) B \(\longrightarrow \) C
where, B is an intermediate nuclei, which is also radioactive. Considering that there are N₀ atoms of A initially, plot the graph showing the variation of number of atoms of A and B versus time.

The isotopes of \({ U }^{ 238 }\ and\ { U }^{ 235 }\) occur in nature in the ratio 140 : 1. Assuming that at the time of earth's formation, they were present in equal ratio, make an estimate of the age of the earth. The half lives of \({ U }^{ 238 }\ and\ { U }^{ 235 }\) are \(4.5\times { 10 }^{ 9 }\) years and \(7.13\times { 10 }^{ 8 }\) years respectively.
Given : \(\log _{ 10 }{ 140 } =2.1461,\log _{ 10 }{ 2 } =0.3010\)

As, we know, an n-type semiconductor has large number of electrons but it is still electrically neutral. Why?

In half wave rectification , what is the output frequency if the input frequency is 50 Hz. What is the output frequency of a full wave rectification for the same input frequency.

What is a ground wave? Why short wave communication over long distance is not possible via ground waves?