*27*

Section E of the **Class 12 CBSE Physics Solved Question Paper** includes **long answer questions**, each worth 5 marks. These questions require detailed explanations, derivations, or multi-step calculations. Practicing these questions will help students develop a thorough understanding of Physics concepts, ensuring they can tackle the most challenging questions in the exam with confidence.

## Section E – Questions 31 to 33

**31 (a).**

i. Draw equipotential surfaces for an electric dipole.

ii. Two point charges *q _{1}* and

*q*are located at

_{2}*r*and

_{1}*r*respectively in an external electric field

_{2}*E*. Obtain an expression for the potential energy of the system.

**31 (b)**. A thin spherical shell of radius *R* has a uniform surface charge density *σ*. Using Gauss’ law, deduce an expression for the electric field (i) outside and (ii) inside the shell.

**32 (a).** You are given three circuit elements X, Y, and Z. They are connected one by one across a given AC source. It is found that *V* and *I* are in phase for element X. *V* leads *I* by *π/4* for element Y, while *I* leads *V* by *π/4* for element Z. Identify elements X, Y, and Z.

**32 (b).** Describe the construction and working of a transformer and hence obtain the relation for *V _{s} / V_{p}* in terms of the number of turns of primary and secondary.

**33 (a).** (i) A plane light wave propagating from a rarer into a denser medium is incident at an angle *i* on the surface separating two media. Using Huygen’s principle, draw the refracted wave and hence verify Snell’s law of refraction.

**33 (a)** (ii). In a Young’s double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the distance between the central bright fringe and the 4th dark fringe.

**33 (b). (i)**. Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.

**33 (b) (ii)**. An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.

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