Answer:
The capacitance per unit length is [tex]5.06\times10^{-11}\ F/m[/tex]
(b) is correct option.
Explanation:
Given that,
Radius a= 2.50 mm
Radius b=7.50 mm
Dielectric constant = 3.68
Potential difference = 120 V
We need to calculate charge per length for the capacitance
Using formula of charge per length
[tex]\lambda=\dfrac{4\pi\epsilon_{0}\Delta V}{2 ln(\dfrac{r_{2}}{r_{1}})}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{120}{9\times10^{9}\times2 ln(\dfrac{7.50\times10^{-3}}{2.50\times10^{-3}})}[/tex]
[tex]\lambda=6.068\times10^{-9}\ C/m[/tex]
We know that,
[tex]\lambda=\dfrac{Q}{L}[/tex]
We need to calculate the capacitance per unit length
Using formula of capacitance per unit length
[tex]C=\dfrac{\dfrac{Q}{L}}{\Delta V}[/tex]
[tex]C=\dfrac{6.068\times10^{-9}}{120}[/tex]
[tex]C=5.06\times10^{-11}\ F/m[/tex]
Hence, The capacitance per unit length is [tex]5.06\times10^{-11}\ F/m[/tex]
