Q. 323.7( 6 Votes )

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 field lines at the ends).

Answer :

Radius of outer cylinder(R) = 1.5cm = 0.015m

Radius of inner cylinder(r) = 1.4cm = 0.014m

Charge on the inner cylinder(q) = 3.5m = 3.5 × 10-6C

Length of a co-axial cylinder(l) = 15cm = 0.15m

Capacitance of a co-axial cylinder of radii R and r, is given as:

where ϵ0 = Permittivity of free space = 8.8510-12N-1 m-2 C2


(Trick: Multiply by 2.303 to convert loge to log10)

C = 1.210-10F

Potential difference of the inner cylinder,

V = 2.29104V

Therefore, Capacitance = 1.210-10F

Potential difference = 2.29104V

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