Question

A 0.350-m-long cylindrical capacitor consists of a solid conducting core with a radius of 1.20 mm and an outer hollow conducting tube with an inner radius of 2.00 mm. The two conductors are separated by air and charged to a potential difference of 6.00 V. Calculate
(a) the charge per length for the capacitor;
(b) the total charge on the capacitor;
(c) the capacitance;
(d) the energy stored in the capacitor when fully charged.

Answer 1

Explanation:

Below is an attachment containing the solution.

Answer 2

Answer: a. 6.52*EXP{-10}C/m. b. 2.28*EXP{-10}C. c. 38picoFarad.

d. 6.84*EXP{-10}joules

Explanation: We first calculate for the capacitance first. For a concetric cylinder with two radius R1 and R2 the capacitance C is given as

C= {2*pi*permitivity of

freespace*lenght}/In(R2/R1) from the given Question R2 is 2mm and R1 is 1.2mm, lenght is 0.35meter, permitivity of free space is 8.85*EXP {-12} and pi is 3.142.

Therefore Capacitance would be,

C = 2*3.142*8.85*EXP

{-12}*0.35/In(2/1.2)

C = 3.8*EXP {-11} Farad which is also

38*EXP {-12} Farad or 38picoFarad.

Next, we solve for our total charge Q. Charge, capacitance and voltage are related by

Q = C*V = 38*EXP {-12}*6

=2.28*EXP {-10} Coulombs

Next, we obtian charge per unit lenght, which is

Q/L = 2.28*EXP {-10}/0.35

= 6.52*EXP {-10} Coulombs/meter

Next, we obtain the energy stored in the capacitor from

Energy stored = 1/2*(C*V²)

=1/2*38*EXP {-12}*6²

=6.84*EXP {-10} Joules

Note: EXP means 10^