In polar molecules, the centres of positive and negative charges of molecule do not coincide. The statement is always

In a permanent magnet at room temperature

Charges of magnitude 2Q and -Q are located at points (a, 0, 0) and (4a, 0, 0). Find the ratio of the flux of electric field due to these charges, through concentric spheres of radii 2a and 8a centered at the origin.

Is it possible that there is no potential difference between the plates of a cell? If yes, under what condition?

If the distance between two parallel current carrying wires is doubled, what is the force between them?

Derive the expression for internal resistance of a cell.

Name three elements required to specify the earth's magnetic field at a given place.Draw a labelled diagram to define these elements.Explain briefly how these elements are determined to find out the magnetic field at a given place on the surface of earth.

Three capacitors of equal capacitance when connected in series have a net capacitance of\({ C }_{ 1 }\).When the same capacitance is\({ C }_{ 2 }\).Find the ratio \(\frac { { C }_{ 1 } }{ { C }_{ 2 } } \)

A solenoid 50 cm long has 4 layers of winding of 350 turns each. The radius of the lowest layer is 1.4 cm. If the current carried is 6.0 A, estimate the magnitude of B
(a) near the centre of the solenoid on its axis, and off its axis.
(b) near its ends on its axis.
(c) outside the solenoid near its centre.

A parallel capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) where\(\varepsilon =\alpha U\\ \) \(\alpha =2{ V }^{ -1 }\\ \).A similar capacitor with no dielectric is charged to \({ U }_{ 0 }=78V\\ \)It is then connected to the uncharged capacitor with the dielectric.Find the final voltage on the capacitors.

What is the e.m.f. of a cell? State the factors on which its value depends. Derive a relation between e.m.f. E, terminal potential difference V, internal resistance r of a cell and external resistance R. Prove that e.m.f. is more than potential difference.

(i) Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence, derive the expression for the kinetic energy acquired by the particles.

Two +ve charge of 0.2\(\mu C\) and 0.01\(\mu C\) are placed 10cm apart.Calculate the work done if reducing the distance to 5cm.

A particle of mass m carrying a charge \(-q_1\) is moving around a charge \(+q_2\) along a circular path of radius r. Prove that period of revolution of charge \(-q_1\) about \(+q_2\) is given by \(T={\sqrt{16\pi^3\epsilon_omr^3\over q_1q_2}}\)

A storage battery of e.m. 12.0V and internal resistance 0.5\(\Omega\)is to be charged by a 120Vd.c. supply of negligible internal resistance. What resistance is required in the circuit for the charging current to be 3A? What is the terminal voltage o the battery during charging?

If the maximum value of accelerating potential provided by a radio frequency oscillator be 25 kV, find the number of revolutions made by a proton in a cyclotron to achieve one sixth of the speed of light. Mass of proton = 1.67 x 10^-27 kg.