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).
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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