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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).

Class 12th NCERT - Physics Part-I 2. Electrostatic Potential and Capacitance

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

Therefore,

(Trick: Multiply by 2.303 to convert log_e 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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