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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 - 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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Solution

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 × 10−6 C

Capacitance of a co-axial cylinder of radii `r_1` and `r_2` is given by relation 

`C=(2piin_ol)/log(r_1/r_2)`

Where,

`in_0`= Permittivity of free space = `8.85xx10^-12 N^-1m^-2C^2`

`therefore C=(2pixx8.85xx10^-12xx0.15)/(2.3026 log_10(0.15/0.14))`

`=(2pixx8.85xx10^-12xx0.15)/(2.3026 xx 0.0299)=1.2xx10^-10 F`

Potential difference of the inner cylinder is given by,

`V=q/C`

`=(3.5xx10^-6)/(1.2xx10^-10)=2.92xx10^4 V`

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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Q 32 | Page 91
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