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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\muC. 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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