A parallel plate capacitor has square plates of side 5 cm and separated by a distance of 1 mm.
(a) Calculate the capacitance of this capacitor.
(b) If a 10 V battery is connected to the capacitor, what is the charge stored in any one of the plates? (The value of ε_o = 8.85 x 10^-12 Nm² C^-2)

Dielectric strength of air is 3 x 10⁶ V m^-1. Suppose the radius of a hollow sphere in the Van de Graff generator is R = 0.5 m, calculate the maximum potential difference created by this Van de Graaff generator.

Five identical charges Q are placed equidistant on a semicircle as shown in the figure. Another point charge q is kept at the center of the circle of radius R. Calculate the electrostatic force experienced by the charge q.

The electrostatic potential is given as a function of x in figure (i) and (ii). (a) Calculate the corresponding electric fields in regions A, B, C and D for the Figure (i). (b) Plot the electric field as a function of x for the figure (ii).

A battery of voltage V is connected to 30 W bulb and 60 W bulb as shown in the figure.
(a) Identify brightest bulb
(b) which bulb has greater resistance?
(c) Suppose the two bulbs are connected in series, which bulb will glow brighter?

A copper wire of 10^-6 m² area of cross section, carries a current of 2 A. If the number of free electrons per cubic meter in the wire is 8\(\times\)10²⁸, Calculate the current density and average drift velocity of electrons.

The rod given in the figure is made up of two different materials.

Both have square cross sections of 3 mm side. The resistivity of the first material is 4 x 10^-3 Ωm and that of second material has resistivity of 5 x 10^-3 Ωm. What is the resistance of rod between its ends?

A particle of charge q moves with velocity\(\vec { v } \) along positive y-direction in a magnetic field \(\vec { B } \) .Compute the Lorentz force experienced by the particle
(a) when magnetic field is along positive y - direction
(b) when magnetic field points in positive z - direction
(c) when magnetic field is in zy - plane and making an angle θ with velocity of the particle. Mark the direction of magnetic force in each case

A proton moves in a uniform magnetic field of strength 0.500 T magnetic field is directed along the x - axis. At initial time, t  = 0s, the proton has velocity
\(\hat { v } =(1.95\times { 10 }^{ -5 }\hat { i } +2.00\times { 10 }^{ 5 }\hat { k } )m{ s }^{ -1 }\). Find
(a) At initial time, what is the acceleration of the proton.
(b) Is the path circular or helical? If helical, calculate the radius of helical trajectory and also calculate the pitch of the helix (Note: Pitch of the helix is the distance travelled along the helix axis per revolution).

A circular coil with cross-sectional area 0.1 cm² is kept in a uniform magnetic field of strength 0.2 T. If the current passing in the coil is 3 A and plane of the loop is perpendicular to the direction of magnetic field. Calculate
(a) total torque on the coil
(b) total force on the coil
(c) average force on each electron in the coil due to the magnetic field. (The free electron density for the material of the wire is 10²⁸ m^–3).

A non - conducting sphere has a mass of 100 g and radius 20 cm. A flat compact coil of wire with turns 5 is wrapped tightly around it with each turns concentric with the sphere. This sphere is placed on an inclined plane such that plane of coil is parallel to the inclined plane. A uniform magnetic field of 0.5 T exists in the region in vertically upward direction. Compute the current I required to rest the sphere in equilibrium.

A 3.0m wire carrying a current of 10A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to the 0.277. What is the magnetic force on the wire?

A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 × 10^–5 Wb, find the magnetic energy stored in the medium surrounding the coil.

A graph between the magnitude of the magnetic flux linked with a closed loop and time is given in the figure. Arrange the regions of the graph in ascending order of the magnitude of induced emf in the loop.

A wheel with 10 metallic spokes each 0.5m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of the earth's magnetic field HE at a place if H_E = 0.4 G at the place what is the induced emf between the a x k and the rim of the wheel? Take 1 gauss (G) = 10^-4T.

A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm, What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)

In Young's double-slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two-wavelength λ₀ = 750 nm and λ = 900mm. What is the minimum distance from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a . bright fringe from the other?

The focal length of an equiconvex lens is equal to the radius of curvature of either face. What is the value of refractive index of the material of the lens?

How many photons per second emanate from a 50 mW laser of 640 nm?

A 150 W lamp emits light of mean wavelength of 5500 Å. If the efficiency is 12%, find out the number of photons emitted by the lamp in one second.

When a 6000Å light falls on the cathode of a photo cell, photoemission takes place. If a potential of 0.8 V is required to stop emission of electron, then determine the
(i) frequency of the light
(ii) energy of the incident photon
(iii) work function of the cathode material
(iv) threshold frequency and
(v) net energy of the electron after it leaves the surface.

Show that the mass of radium \((_{ 88 }^{ 226 }{ Ra })\) with an activity of 1 curie is almost a gram. Given T_1/2 = 1600 years.

A transistor having α = 0.99 and V_BE = 0.7V, is connected in the common-cmiitter configuration as shown in figure. If the transister is in saturation region, find the value of the collector current.

What is meant by satellite communication? Give its applications.