(a) (i) Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $$\lambda$$.

(ii) An infinitely long positively charged straight wire has a linear charge density $$\lambda$$. An electron is revolving in a circle with a constant speed $$v$$ such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of magnitudes of its charge and linear charge density $$\lambda$$ on the wire.

(iii) Draw a graph of kinetic energy as a function of linear charge density $$\lambda$$.

OR

(b) (i) Consider two identical point charges located at points $$(0,0)$$ and $$(a, 0)$$.

(1) Is there a point on the line joining them at which the electric field is zero?

(2) Is there a point on the line joining them at which the electric potential is zero?

Justify your answers for each case.

(ii) State the significance of negative value of electrostatic potential energy of a system of charges.

Three charges are placed at the corners of an equilateral triangle $$A B C$$ of side $$2.0 \mathrm{~m}$$ as shown in figure. Calculate the electric potential energy of the system of three charges.

(a) (i) Define coefficient of self-induction. Obtain an expression for self-inductance of a long solenoid of length $$l$$, area of cross- section A having $$\mathbf{N}$$ turns.

(ii) Calculate the self-inductance of a coil using the following data of obtained when an AC source of frequency $$\left(\frac{200}{\pi}\right) \mathrm{~Hz}$$ and a DC source is applied across the coil.

OR

(b) (i) With the help of a labelled diagram, describe the principle and working of an ac generator. Hence, obtain an expression for the instantaneous value of the emf generated.

(ii) The coil of an ac generator consists of 100 turns of wire, each of area $$0.5 \mathrm{~m}^2$$. The resistance of the wire is $$100 \Omega$$. The coil is rotating in a magnetic field of $$0.8 \mathrm{~T}$$ perpendicular to its axis of rotation, at a constant angular speed of 60 radian per second. Calculate the maximum emf generated and power dissipated in the coil.

(ii) Calculation of self inductance:

(a) (i) State Huygen's principle. With the help of a diagram, show how a plane wave is reflected from a surface. Hence, verify the law of reflection.

(ii) A concave mirror of focal length $$12 \mathrm{~cm}$$ forms a three times magnified virtual image of an object. Find the distance of the object from the mirror.

OR

(b) (i) Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power. Write two limitations of a refracting telescope over a reflecting telescope.

(ii) The focal lengths of the objective and the eyepiece of a compound microscope are $$1.0 \mathrm{~cm}$$ and $$2.5 \mathrm{~cm}$$ respectively. Find the tube length of the microscope for obtaining a magnification of 300.

(a) Consider the experimental set up shown in the figure. This jumping ring experiment is an outstanding demonstration of some simple laws of Physics. A conducting non-magnetic ring is placed over the vertical core of a solenoid. When current is passed through the solenoid, the ring is thrown off.

Answer the following questions :

(i) Explain the reason of jumping of the ring when the switch is closed in the circuit.

(ii) What will happen if the terminals of the battery are reversed and the switch is closed? Explain.

(iii) Explain the two laws that help us understand this phenomenon.

OR

(b) Briefly explain various ways to increase the strength of magnetic field produced by a given solenoid.