question_answer

Write down the expression for capacitance of a spherical capacitor whose conductors radii are \[{{R}_{1}}\] and \[{{R}_{2}}({{R}_{1}}>{{R}_{2}}),\]when inner sphere is grounded

A)  \[\frac{4\pi {{\varepsilon }_{0}}{{R}_{1}}{{R}_{2}}}{{{R}_{2}}-{{R}_{1}}}\]                              

B)  \[\frac{4\pi {{\varepsilon }_{0}}R_{1}^{2}}{{{R}_{2}}-{{R}_{1}}}\]

C)  \[\frac{4\pi {{\varepsilon }_{0}}R_{2}^{2}}{{{R}_{2}}-{{R}_{1}}}\]                              

D)  \[\frac{4\pi {{\varepsilon }_{0}}R_{1}^{2}{{R}_{2}}}{{{({{R}_{2}}-{{R}_{1}})}^{2}}}\]

Correct Answer: C

Solution :

\[{{C}_{system}}={{C}_{AB}}+{{C}_{B\infty }}\] \[=\frac{4\pi {{\varepsilon }_{0}}{{R}_{1}}{{R}_{2}}}{{{R}_{2}}-{{R}_{1}}}=4\pi {{\varepsilon }_{0}}{{R}_{2}}\] \[=\frac{4\pi {{\varepsilon }_{0}}R_{2}^{2}}{{{R}_{2}}-{{R}_{1}}}\]