Question

A cylindrical capacitor consists of a solid inner conducting core with radius 0.220 cm , surrounded by an outer hollow conducting tube. The two conductors are separated by air, and the length of the cylinder is 13.5 cm . The capacitance is 36.5 pF .

Part A

Calculate the outer radius of the hollow tube.

Part B

When the capacitor is charged to 150 V , what is the charge per unit length λ on the capacitor?

PART B IS THE IMPORTANT

Answer 1

Sol::

Let inner radius be (a)= 0.22 cm =0.0022 m

And outer radius be= b

A)

Capacitance/unit length of a long cylinder is

C/L = (2πεrε₀) / (ln (b/a))

Where
b is radius of outside conductor
a is radius if inside conductor
ε₀ = 8.85*10^-12 F/m
εᵣ =1( dielectric constant, vacuum = 1)
C = 36.5 pF
So,

36.5*10^-12/0.135 = (2π*1*8.85*10^-12) / (ln (b/a))
36.5*10^-12 = 0.135(55.606*10^-12)/(ln (b/a))

ln (b/a) = 0.2056
b/a = 1.2282
b = 1.2282*a
=1.2282*0.0022
= 0.00270 m
=0.27 cm

B)

Second half, using Q = CV we will get charge and ,so dividing it by 13.5 cm will get charge per cm.
i. e Q=(36.5*10^-12)*(150)
=5475*10^-12 C
= 5475 pC
So, charge per unit length
λ =Q/L
= (5475*10^-12)/0.135
=40555.55*10^-12 C/m
=40.55*10^-9 C/m

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