21.

a) Two point charges Q₁ = 400  and Q₂ = 100  are kept fixed, 60 cm apart in vacuum.Find intensity of the electric field at midpoint of the line joining Q₁ and Q₂.
b) i) State Gauss' law.

ii) In an electric dipole, at which point is the electrical potential zero?

22.

a) Obtain an expression for equivalent capacitance when three capacitors C₁, C₂ and C₃ are connected in series.

b) A metallic wire has a resistance of 3.0 ohm and 0^o Cand 4.8 ohm at 150^o C. Find the temperature coefficient of resistance of its material?

23. a) In the circuit shown in figure E₁ and E₂ are two cells having emfs 2 V and 3 V respectively, and negligible internal resistances. Applying Kirchoff's laws of electrical networks, find the values of currents I₁ and I₂.
 
b) State how a moving coil galvanometer can be converted into an ammeter.

24.

a) Draw a labelled circuit diagram of a potentiometer to measure internal resistance of a cell. Write the working formula.

b) i) Define Curie temperature.
ii) If magnetic susceptibility of a certain magnetic material is 0.0001, find its relative permeability.

25.

i) Two infinitely long current carrying conductors X and Y are kept parallel to each other, 24 cm apart in vacuum. They carry currents of 5 A and 7 A respectively, in the same direction, as shown in the figure below. Find the position os a neutral point, i.e., a point where resultant magnetic flux density is zero.



ii) If current through the conductor Y is reversed in direction, will neutral point lie between x and Y, to the left of X or to the left of Y?

26.

i) Define Ampere in terms of force between two current carrying conductors.

ii) What is an ideal transformer.

27.

a) A coil having self-inductance of 0.7 H and resistance of 165 ohm is connected to an ac source of 275 V, 50 Hz. If .
Calculate:

i) reactance of the coil
ii) impedance of the coil
iii) current flowing through the coil

b) Draw a labelled graph showing variation of impedance of a series LCR circuit with frequency of the a.c. supply.

28.

a) Derive Snell's law of refraction using Huygen's wave theory.

b) Monochromatic light of wavelength 650 nm falls normally on a slit of width 1.3 x 10^-4 and the resulting Fraunhofer diffraction is obtained on a screen. Find the angular width of the central maxima.

29.

a) In Young's Double Slit experiment, show that:

, where the terms have their usual meaning.
b) A ray of ordinary light is travelling in air. It is incident on air-glass pair at a polarising angle of 56^o. Find the angle of refraction in glass.

30. a) Find the angle of incidence at which a ray of monochromatic light should be incident on the first surface AB of a regular glass prism ABC so that the emergent ray grazes the adjacent surface AC. (Refractive index of glass = 1.56)

b) State how focal length of glass lens (refractive index 1.5) changes when it is completely immersed in:
i) Water (Refractive Index 1.33)
ii) A liquid (Refractive index 1.65)