Q10E - University Physics with Modern Physics

Question

A cylindrical capacitor consists of a solid inner conducting core with radius of 0.250 cm, surrounded by an outer hollow conducting tube. The two conductors are separated by air, and the length of the cylinder is 12.0 cm. The capacitance is 36.7 pF. 

(a) Calculate the inner radius of the hollow tube. 

(b) When the capacitor is charged to 125 V, what is the charge per unit length l on the capacitor?

Step-by-Step Solution

Answer

The capacitance of the coaxial axis is 0.3cm.

The charge per unit length is $38.2nC/m$.

Step 1: Capatince of coaxial axis.

Given $r_a=0.25cm,L=12.0cm,C=36.7\times {10}^{-12}C/V$

The capacitance of the co-axial cylinder is given by

Substitute in equation(1)

Now simplify by taking exponential function for both sides to get

Therefore, the capatiance of the coaxial axis is 0.3cm.

Step 2: About charge per unit length.

lf the potential is 125.0V then the total charge Q is given by

$Q=\lambda L=CV=>\left(3\right)$

Substitute in equation(3)

Hence, the charge per unit length is 38.2n C/m.