Spherical Capacitors: Practice Problem & Solution
Assertion (A): In a system of two concentric shell of inner radius \(a\) and outer radius \(b\). If outer is grounded and inner shell is given charge has less capacitance than inner has grounded and outer is given charge. Reason (R): Electric field is zero outside outer shell when inner shell is grounded.
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:
A: True. For inner charged, outer grounded, \(C_1 = 4\pi\epsilon_0 \frac{ab}{b-a}\). For inner grounded, outer charged, \(C_2 = 4\pi\epsilon_0 \frac{b^2}{b-a}\). Since \(b>a\), \(C_1 < C_2\).\nR: False. If the outer shell is given charge, there will be a net charge creating an external electric field.\nTherefore, (A) is true and (R) is false.
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