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).

Answers (1)

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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