The capacitance of a system of two identical metal balls of radius a is given by following relation
$X π ϵ_{o} ϵ_{r} a$
Find the value of X if the distance between their centres is equal to b , with $b ≫ a$ . The system is located in a uniform dielectric with permittivity $ε$ .

Question

The capacitance of a system of two identical metal balls of radius a is given by following relation

$X π ϵ_{o} ϵ_{r} a$

Find the value of X if the distance between their centres is equal to b , with $b ≫ a$ . The system is located in a uniform dielectric with permittivity $ε$ .

TestHub · Accepted Answer

b ≫ a so we can assume surface charge density constant V 1 ​ = a kq ​ + b k ( − q ) ​ V 2 ​ = a k ( − q ) ​ + b kq ​ Δ V = V 1 ​ − V 2 ​ = a 2 kq ​ − b 2 kq ​ 2 kq ( a 1 ​ − b 1 ​ ) □ a 2 Kq ​ q = C ( a 2 Kq ​ ) C = 2 Kq q. a ​ = 2 ( 4 π ϵ o ​ ϵ r ​ 1 ​ ) a ​ = 2 π ϵ o ​ ϵ r ​ a

Physics - Capacitor Question with Solution | TestHub

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