A metal rod of square cross-sectional area A having length l has current I flowing through it when a potential difference of V volt is applied across its ends (figure I). Now the rod is cut parallel to its length into two identical pieces and joined as shown in figure II. What potential difference must be maintained across the length 2l so that the current in the rod is still I?

The wavelength λ of a photon and the de-Broglie wavelength of an electron have the same value. Show that energy of a photon is (2λmc/h) times the kinetic energy of electron; where m, c and h have their usual meaning.

Distinguish between polarized and unpolarised light. Does the intensity of polarized light emitted by a polaroid depend on its orientation? Explain briefly.

The vibrations in a beam of polarized light make an angle of 60° with the axis of the polaroid sheet. What percentage of light is transmitted through the sheet?

(a) Define torque acting on a dipole of dipole moment p placed in a uniform electric field

Express it in the vector form and point out the direction along which it acts.

(b) What happens if the field is non-uniform?

(c) What would happen if the external field is increasing (i) parallel to and (ii) anti-parallel to ?

(a) A point charge q moving with speed v enters a uniform magnetic field that is acting into the plane of the paper as shown. What is the path followed by the charge q and in which plane does it move?

(b) How does the path followed by the charge get affected if its velocity has a component parallel to?

(c) If an electric field is also applied such that the particle continues moving along the original straight-line path, what should be the magnitude and direction of the electric field ?