Question

Three long concentric conducting cylindrical shells have radii r, 2r, 2√2r onner and outer shells are connected to each other .The capacitance across middle and inner shells per unit lengths is

Answer 1

Answer:

The answer is 6π∈0 / ln2.

Step-by-step explanation:

The capacitance between the inner and middle shell is equal to equivalent capacitance when C1 and C2 are connected parallel.

Capacitance per unit length of cylindrical capacitor C=2π∈0 / lnR2/R1  

C1 = 2π∈0 / ln(2R/R)  = 2π∈0 / ln2

C2 = 2π∈0 / ln (2√2 R/ 2R)  

After cancellation it will become.

C2 = 2π∈0 / ln√2

As it is a combination of two capacitors connected in parallel. Therefore,

Ceq=C1+ C2

=2π∈0 / ln2 + 2π∈0 / ln√2

Ceq =6π∈0 / ln2

Answer 2

Solution in attachment

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