Concepts Of Physics MCQ Edition [Volume 2]PhysicsCapacitors
An arrangement consists of three conducting concentric spherical shells with radii a , b , and c , as depicted in the figure. The region between the two inner shells is filled by a dielectric of dielectric constant K . Determine the capacitance of the system between A and B .
Options
- A4 ₀ K a b c K a (c - b) + c(b - a)
- B4 ₀ b [K a(c - b) + c(b - a)] (b - a)(c - b)
- C4 ₀ K a b c a (c - b) + K c(b - a)
- D4 ₀ a b c K a (c - b) + c(b - a)
Correct answer
A. 4 ₀ K a b c K a (c - b) + c(b - a)
Step-by-step solution
The given arrangement can be considered as two spherical capacitors connected in series. The first capacitor C₁ is formed by the inner shell of radius a and the middle shell of radius b . The space between them is filled with a dielectric of constant K . Its capacitance is: C₁ = 4 ₀ K a b b - a The second capacitor C₂ is formed by the middle shell of radius b and the outer shell of radius c . The space between them is vacuum (or air). Its capacitance is: C₂ = 4 ₀ b c c - b Since the terminals A and B are connected