The Kinetic Theory Of Gases

Step 1: Since , fringe effects are neglected. The capacitor can be treated as a parallel combination of infinitesimal capacitors along the horizontal direction.
Step 2: Consider a thin vertical strip of width at a distance from the left end. The height of dielectric in this strip increases linearly from to :
Step 3: The infinitesimal capacitance of this strip is: where the effective permittivity varies continuously from to .
Step 4: The equivalent capacitance is obtained by integrating:
Step 5: Simplify and integrate:
Step 6: Evaluating the limits:

Step 1: For electrostatic equilibrium, field inside conductor = 0.
Step 2: Charge enclosed by outer conductor must be neutralized on its inner surface. Total charge inside outer shell:
Step 3: To cancel this, inner surface must have: Hence → (D).

Step 1: Recall how sound propagates. Sound is a mechanical wave and requires a material medium to travel. It cannot propagate in a vacuum. Step 2: Compare the speed of sound in different media. The speed of sound depends on the elasticity and density of the medium: Step 3: Analyze the given options.

(A) Water (liquid) — faster than air, slower than solids
(B) Air (gas) — slowest among material media
(C) Metal (solid) — highest speed ✔
(D) Vacuum — sound cannot travel
Step 4: Final conclusion. The velocity of sound is largest in metal.