Long Type Questions(3 marks)

- Define electric field intensity at a point. Derive an expression for the electric field intensity at a point on the axial line of a short dipole.
- Show that the potential on the equatorial line of an electric dipole is zero
- What is an electric dipole? Derive an expression for the torque acting on an electric dipole, when held in a uniform electric field. Hence, define the dipole moment.
- State Gauss theorem in electrostatics. Using this theorem, derive an expression for the electric field intensity due to an infinite plane sheet of charge of charge density σ
- Show mathematically that for any point out side the shell, the field due to a uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre.
- Apply gauss theorem to find electric field intensity at a point due to an infinitely long thin, uniformly charged straight wire.
- Define the capacitance of a capacitor. Give its S.I unit for a parallel plate capacitor, prove that the total energy stored in a capacitor is ½ cv
_{2}and hence derive expression for the energy density of the capacitor. - Derive an expression for the capacitance of a parallel plate capacitor when the space between the plates is partially filled with a dielectric medium of dielectric constant k.
- Obtain the equivalent capacitance of the network in figure shown below. For a 300V supply determine the charge and voltage across each capacitor.
- Give the principle of working of a Van –De – Graff generator. With the help of a labeled diagram describe its construction and working. How is the leakage of charge minimized from the generator?
- Establish a relation between drift velocity of an electron in a conductor of cross section A carrying current I and concentration ‘n’ of free electrons per unit volume of conductor.
- Define the term resistivity and write its S.I unit. Derive the expressions for
- resistance
- the resistivity of a conductor in terms of number density of free electrons and relaxation time.

- Draw a circuit diagram for a meter bridge two determine the unknown resistance of a resistor why are the connections between the resistors of a meter bridge made of thick copper strips? Find the shift in the balance point of a meter bridge, when the two resistors in the two gaps are interchanged.
- With the help of a circuit diagram explain how the internal resistance of a cell can be determine by using a potentiometer? Write the formula used?
- Show graphically the variation of resistivity with temperature for
- Metals
- alloys
- semi conductors
- non conductor (carbon)

- Why is potentiometer preferred over voltmeter to measure the emf of a cell? The potentiometer wire AB shown in the fig. is 400 cm long. Where should the free end of a galvanometer be connected so that the galvanometer shows zero deflection.
- Derive the relation between the focal length of a convex lens in terms of the radii of curvature of the two surfaces and refractive index of its material. A convex lens of focal length 40 cm and a concave lens of focal length 25 cm are kept in contact with each other. What is the value of power of this combination?
- State the essential condition for diffraction of light to take place. Use Huygen's principle to explain diffraction of light due to a narrow single slit and the formation of a pattern of fringes obtained on the screen. Sketch the pattern of fringes formed due to diffraction at a single slit showing variation of intensity with angle.
- State Huygens’ principle. Using the geometrical construction of secondary wavelets, explain the refraction of a plane wave front incident at a plane surface. Hence verify laws of reflection and refraction.
- With the help of a ray diagram, show the formation of image of a point object by refraction of light at a spherical surface separating two media of refractive indices n
_{1}and n_{2}(n_{2}> n_{1}) respectively. Using this diagram, derive the relation.What happens to the focal length of convex lens when it is immersed in water? - Define the term dipole moment of an electric dipole indicating its direction. Write its SI unit. An electric dipole is placed in a uniform electric field, Deduce the expression for the torque acting on it. In a particular situation, it has its dipole moment aligned with the electric field. Is the equilibrium stable or unstable?
- Obtain the expression for the capacitance of a parallel plate capacitor. Three capacitors of capacitances C
_{1}, C_{2}and C_{3}are connected- in series,
- in parallel. Show that the energy stored in the series combination is the same as that in the parallel combination.

- Define the term magnetic inclination (Dip) and horizontal component of earth’s magnetic field at a place. Establish the relationship between them with the help of a diagram.
- Distinguish the magnetic properties of dia, para, and ferromagnetic substances in terms of
- susceptibility
- magnetic permeability
- coercivity. Give one example of each.

- Derive a mathematical expression for the force per unit length experienced by each of the two long current carrying conductors placed parallel to each other in air. Hence define one ampere of current. Explain why two parallel straight conductors carrying current in the opposite direction kept near each other in air repel?
- With the help of a neat and labelled diagram, explain the underlying principle and working of a moving coil galvanometer. What is the function of:
- uniform radial field
- soft iron core, in such a device? Write two factors on which the current sensitivity of a moving coil galvanometer depend.

- Draw a neat and labelled diagram of a cyclotron. State the underlying principle and explain how a positively charged particle gets accelerated in this machine. Show mathematically that the cyclotron frequency does not depend upon the speed of the particle.
- State the Biot - Savart law for the magnetic field due to a current carrying element. Use this law, obtain a formula for magnetic field
- at the centre of a circular loop of radius R carrying a steady current I. Sketch the magnetic field lines for a current loop clearly indicating the direction of the field.
**OR** - derive the expression for the magnetic field due to a current carrying circular loop of radius 'R', at a point which is at a distance 'x' from its centre along the axis of the loop.

- at the centre of a circular loop of radius R carrying a steady current I. Sketch the magnetic field lines for a current loop clearly indicating the direction of the field.
- Derive an expression for the torque acting on a loop of N turns, area A, carrying current i, when held in a uniform magnetic field. With the help of circuit, show how a moving coil galvanometer can be converted into an ammeter of given range. Write the necessary mathematical formula.
- Derive the expression for the de Broglie wavelength of an electron moving under a potential difference of V volt. Describe Davisson and Germer experiment to establish the wave nature of electrons. Draw a labelled diagram of the apparatus used.
- State the principle of working of p-n diode as a rectifier. Explain, with the help of a circuit diagram, the use of p-n diode as
- a full wave rectifier
- Half wave rectifier. Draw a sketch of the input and output waveforms.

- State Bohr’s postulates for an atom? Calculate energy of moving electron for nth orbit? What is the significance of negative energy?
- State Gauss’ theorem in electrostatics. Using this theorem, derive the expression for the electric field intensity
- at any point outside a uniformly charged thin spherical shell
- at a point due to an infinitely long, thin, uniformly charged straight wire
- at a point due to an infinite plane sheet of charge.

- What is a phasor diagram? With its help, drive an expression for the impedance of an ac series L-c-R circuit. In series LCR circuit, voltage across an inductor, a capacitor and a resistor are 30v, 30v and 60v respectively. What is the phase difference between the applied voltage and current in the circuit.

**
**