Class 12 Physics, CBSE and UP Board, Electrostatic Potential and Capacitance, Additional Exercise,Chapter-2 Exercise 2.32,NCERT Solutions for Class 12 Physics
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).
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Length of a co-axial cylinder, l= 15 cm = 0.15 m
Radius of outer cylinder, r1 = 1.5 cm = 0.015 m
Radius of inner cylinder,r2 = 1.4 cm = 0.014 m
Charge on the inner cylinder, q = 3.5 μC = 3.5 x 10-6 C
Capacitance of a co-axial cylinder of radii r1 and r2 is given by the relation
C = (2πε0 l)/loge(r1/r2)
Where,
ε0= Permittivity of free space = 8.85 x 10⁻¹² N⁻¹m⁻² C²
Therefore C =2π (8.85 x 10⁻¹² x 0.15)/2.3026 log10 (0.15/0.14)
=2π (8.85 x 10⁻¹² x 0.15)/2.3026 0.0299
= 1.2 x 10⁻¹⁰ F
Potential difference of the inner cylinder is given by,
V=q/C = (3.5 x 10-6) /(1.2 x 10⁻¹⁰)
=2.92 x 10⁴ V
2.3026×0.0299
Potential difference of the inner cylinder is given by,