In the given figure, calculate the total flux of the electrostatic field through the sphere `S_1` and `S_2`. The wire AB, as shown here, has a linear charge density `lambda` given by `lambda = kx`, where x is the distance measured along the wire, from the end A.

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density lambda without using Gauss’s law.

S_1 and S_2 are two parallel concentric spheres enclosing charges Q and 2Q respectively as shown in the figure. what is the ratio of the electric flux through S_1 and S_2 ?

A vessel ABCD of 10 cm width has two small slits S_(1) and S_(2) sealed with idebtical glass plates of equal thickness. The distance between the slits is 0.8 mm. POQ is the line perpendicular to the plane AB and passing through O, the middle point of S_(1) and S_(2) . A monochromatic light source is kept at S, 40 cm below P and 2 m from the vessel, to illuminate the slits as shown in the figure. Calculate the position of the central bright fringe on the other wall CD with respect of the line OQ. Now, a liquid is poured into the vessel and filled up to OQ. The central bright fringe is fiund to be at Q. Calculate the refractive index of the liquid.

Two concentric spherical shells S_1 and S_2 enclose charge Q and 2Q as shown in the figure If air is inside the tow shells, what is the ratio of electric flux through S_1 and S_2 ?

An electron gun G emits electons of energy 2 keV travelling in the positive x-direction. The electons are required to hit the spot S where GS=0.1 m, and the line GS makes an angle of 60^@ with the x-axis as shown in figure. A uniform magnetic field B parallel to GS exists in the region outside the electron gun.

A thin circular ring of radius r is charged uniformaly so that its linear charge density becomes lambda . Derive an expression for the electric for the electric field at a point P at a distance x from it along the axis of the ring. Hence, prove that at large distances (x>>r), the ring behaves as a point charge.

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 m s^-2 .

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . For the coil in the position shown in the figure. calculate the magnitude of the force on (i) side AB of the coil and (ii) side BC of the coil.

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . Use your answer to show that the magnetic flux density B between the poles of the magnet is 70 mT.

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . The current in the coil in (a) is switched off and the coil s positioned as shown in the figure. The coil is then turned thorugh an angle of 90^@ in a time of 0.14 s. Calculate the average e.m.f. induced in the coil.