The earth revolves around the sun in an orbit of radius $1.5 \times 10^{11} \mathrm{~m}$ with orbital speed $30 \mathrm{~km} / \mathrm{s}$. Find the quantum number that characterises its revolution using Bohr's model in this case (mass of earth $\left.=6.0 \times 10^{24} \mathrm{~kg}\right)$

(a) Write Einstein's photoelectric equation. How did Millikan prove the validity of this equation?

(b) Explain the existence of threshold frequency of incident radiation for photoelectric emission from a given surface.

(a) Define the term 'electric flux' and write its dimensions.

(b) A plane surface, in shape of a square of side 1 cm is placed in an electric field $\vec{E}=\left(100 \frac{\mathrm{~N}}{\mathrm{C}}\right) \hat{i}$ such that the unit vector normal to the surface is given by $\hat{n}=0.8 \hat{i}+0.6 \hat{k}$. Find the electric flux through the surface.

(a) (i) State Lenz's Law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it as per the law of conservation of energy. Justify.

(ii) A metal rod of length 2 m is rotated with a frequency $60 \mathrm{rev} / \mathrm{s}$ about an axis passing through its centre and perpendicular to its length. A uniform magnetic field of 2 T perpendicular to its plane of rotation is switched-on in the region. Calculate the e.m.f. induced between the centre and the end of the rod.

OR

(b) (i) State and explain Ampere's circuital law.

(ii) Two long straight parallel wires separated by 20 cm , carry 5 A and 10 A current respectively, in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.