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# 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

2.32 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$\mu$C. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

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Given

Length of cylinder $l=15cm$

inner radius $a=1.4cm$

outer radius $b=1.5cm$

Charge on the inner cylinder $q=3.5\mu C$

Now as we know,

The capacitance of this system is given by

$C=\frac{2\pi \epsilon _0l}{2.303log_{10}(b/a)}$

$C=\frac{2\pi *8.854*10^{-12}*15*10^{-2}}{2.303log_{10}(1.5*10^{-2}/1.4*10^{-2})}=1.21*10^{-10}F$

Now

Since the outer cylinder is earthed the potential at the inner cylinder is equal to the potential difference between two cylinders.

SO

Potential of inner cylinder:

$V=\frac{q}{C}=\frac{3.5*10^{-6}}{1.21*10^{-10}}=2.89*10^4V$

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