Concentric Shell Capacitance – Rankers Physics

Spherical Capacitors: Practice Problem & Solution

Assertion (A): When outer grounded shell of a two charged concentric shell system is removed, the capacitance of system decreases. Reason (R): Electric field will spread in vast region till infinity.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Spherical Capacitors. Understanding the underlying formula is key to arriving at the correct answer below:

For a concentric spherical capacitor, capacitance is \( C = \frac{4\pi\epsilon_0 ab}{b-a} \). When the outer shell (radius \( b \)) is removed, it becomes a single isolated sphere of radius \( a \), and its capacitance is \( C' = 4\pi\epsilon_0 a \). Since \( \frac{b}{b-a} > 1 \), \( C > C' \), so capacitance decreases. The electric field now extends to infinity, which explains the decrease in capacitance. Thus, (A) is true and (R) is a correct explanation.

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