# 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

Numerical

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).

#### 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 r1 and r2 is given by relation

C = (2piin_0"l")/log_"e"("r"_1/"r"_2)

Where,

in_0 = Permittivity of free space = 8.85 xx 10^-12  "N"^-1  "m"^-2  "C"^2

∴ C = (2pi xx 8.85 xx 10^-12 xx 0.15)/(2.3026 log_10(0.15/0.14))

= (2pi xx 8.85 xx 10^-12 xx 0.15)/(2.3026 xx 0.0299) = 1.2 xx 10^-10  "F"

Potential difference of the inner cylinder is given by,

"V" = "q"/"C"

= (3.5 xx 10^-6)/(1.2 xx 10^-10) = 2.92 xx 10^4  "V"

Concept: Combination of Capacitors
Is there an error in this question or solution?

#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 2 Electrostatic Potential and Capacitance
Exercise | Q 2.32 | Page 91
NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Exercise | Q 32 | Page 91

Share