SAMPLE PAPER

What is meant by ‘detection’ of amplitude modulated wave? Describe briefly the essential steps for detection.

Derive an expression for potential due to a dipole for distances large compared to the size of the dipole. How is the potential due to a dipole different from that due to a single charge?

Obtain an expression for potential energy of a system of two charges in an external field. A system consisting of two chargs $7\mu \mathrm{C}$ and $-2\mu \mathrm{C}$ are placed at $(-9 \mathrm{cm}, 0,0)$and $(9 \mathrm{cm},0,0)$ respectively in an external electric field $\mathrm{E} =\mathrm{A} (1/{\mathrm{r}}^2)$where $\mathrm{A}=9\times 105 \mathrm{C} {\mathrm{m}}^2$. Calculate the potential energy of this system.

Define the ‘self-inductance’ of a coil. Obtain an expression for self-inductance of a long solenoid of cross-sectional area $\mathrm{A}$, length $l$ having $n$ turns for unit length. Prove that self-inductance is the analog of mass in mechanics.

Define the mutual inductance’ of two coils. On what factors does it depend? Two concentric circular coils, one of small radius $r_1$ and the other of large radius $r_2$, such that $r_1<<r_2$, are placed co-axially with centers coinciding. Obtain the mutual inductance of the arrangement.

Draw a ray diagram to show two refractions of light through a glass prism. Explain with help of a diagram the dependence of angle of deviation on the angle of incidence. Hence obtain the relation for the angle of minimum deviation in terms of angle of prism and refractive index of prism.

Using the relation for refraction at a single spherical refracting surface, derive the lens maker’s formula.

Double convex lenses are to be manufactured from a glass of refraction index $1.55$ with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be $20.0 \mathrm{cm}$?