CBSE Class 12 Physics — Long Answer Questions

(a) An electric dipole consists of two point charges q and $-q$ separated by a distance $2a$. Derive an expression for the electric field E due to this dipole at a point distant r from the centre of the dipole on the equatorial plane. Write the expression for the electric field at a far off point, i.e. $r \gg a$. (b) A dipole is placed in x-y plane such that charges q and $-q$ are located at $x = a$ and $x = b$ respectively. There exists an electric field $E = 2\hat{i}\text{ N/C}$ in the region. Calculate the force F and torque τ experienced by the dipole. OR (a) Two cells of emf $E_1$ and $E_2$ with internal resistances $r_1$ and $r_2$ respectively, are connected in parallel by connecting their positive terminals together and negative terminals together. Deduce an expression for equivalent emf and equivalent internal resistance of the combination. (b) A parallel combination, as stated in (a) above, of two cells of emfs $E$ and $3E$ and internal resistances R each is connected across a resistance $2R$. Find the current that flows through resistance $2R$.

(a) Using the relation for refraction at a curved spherical surface, derive the expression for lens maker's formula. (b) Three lenses $L_1$, $L_2$ and $L_3$, each of focal length 40 cm, are placed coaxially. The distance between $L_1$ and $L_2$ and between $L_2$ and $L_3$ are 120 cm and 20 cm respectively. An object is kept at a distance of 80 cm to the left of lens $L_1$. Find the distance of the final image formed from the object. OR (a) Draw a ray diagram to show the image formation by a concave mirror when the object is kept between its focus and the centre of curvature. Using this diagram, derive the mirror formula. (b) A concave mirror produces a two times magnified virtual image of an object kept 10 cm in front of it. Calculate the focal length of the mirror.

(a) State Faraday's law of electromagnetic induction. (b) Derive an expression for the self-inductance of an air-filled long solenoid of length l and cross-sectional area A having N turns. (c) A conducting rod of length 50 cm, with one end pivoted, is rotated with angular speed of 60 rpm in a uniform magnetic field of 4.0 mT directed perpendicular to the plane of rotation of rod. Find the emf induced in the rod. OR (a) Draw a labelled diagram of a step-up transformer. State the principle on which it works and obtain the ratio of secondary voltage to primary voltage in terms of number of turns and currents in the two coils. (b) The ratio of the number of turns in the primary to the secondary of an ideal transformer is $1 : 5$. If 5 kW power at 200 V is supplied to the primary, find (i) current in the primary, and (ii) output voltage.