Question

Question 2.32: 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 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-91

Answer 1

capacitance of cylindrical capacitor is given by
$\mathbb{C}=\frac{2\pi\epsilon_0L}{2.303log_{10}\frac{b}{a}}$
here, a and b are the radii of cylindrical capacitor. where b > a .
L is the length of cylindrical capacitor.

now, $C=\frac{2\times3.14\times8.85\times10^{-12}\times15\times10^{-2}}{2.303log_{10}\frac{1.5}{1.4}}\\\\C=1.21\times10^{-10}F$

electric potential of the inner cylinder is
$V=\frac{Q}{C}=\frac{3.5\times10^{-6}C}{1.21\times10^{-10}F}=2.89\times10^4V$

Answer 2

Answer:

Length of a co-axial cylinder, l=15cm=0.15m

Radius of outer cylinder, r

1

=1.5cm=0.015m

Radius of inner cylinder, r

2

=1.4cm=0.014m

Charge on the inner cylinder, q= 3.5 µC

Capacitance of coaxial cylinder,

C=

ln(r

1

/r

2

)

2πε

o

l

=1.2×10

−10

F

Potential of the inner cylinder is given by,

V=

C

q

=2.92×10

4

V .