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NCERT Class XII Chapter
Electrostatic Potential and Capacitance
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Question : 32 of 37
Marks: +1, -0
A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 μC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e. bending of the field lines at the ends).
Solution:  
Capacitance of cylindrical capacitor is
C = 2πε0L2.303log⁡10ba\frac{2\pi\varepsilon_0 L}{2.303\log_{10}\frac{b}{a}} = 2×15×10−29×109×2.303×log⁡101.51.4\frac{2 \times 15 \times 10^{-2}}{9 \times 10^9 \times 2.303 \times \log_{10}\frac{1.5}{1.4}} or C = 1.21 × 10−1010^{-10} F
Electric potential of the inner cylinder is
V = QC\frac{Q}{C} = 3.5×10−6C1.21×10−10F\frac{3.5 \times 10^{-6} C}{1.21 \times 10^{-10} F} or V = 2.89 × 10410^4 V
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