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Two metal balls of the same radius a are...

Two metal balls of the same radius `a` are located in a homongenous poorly conducting medium with resistivity `rho`. Find the resistance of the medium between the balls provided that the separation between them is mush greater than the radius of the ball.

Text Solution

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Magnitude of the field strength is given by,
`E = ( q)/( 4pi epsilon_(0)a^(2))`
So, current density `j= (1)/(rho)(q)/(4pi epsilon_(0)a^(2))` and electric current
`l = int vec(j).vec(dS)= jS = (q)/( rho 4 pi epsilon_(0)a^(2)).4pi a^(2) = (q)/(rhoepsilon_(0))`
But, potential difference between the balls,
`V_(+) - V_(-) = 2 (q)/( 4pi epsilon_(0)a)`
Hence, the sought resistance
`R = (V_(+) - V_(-))/(l )= ((2q)/(4pi epsilon_(0)a))/((q)/( rho epsilon_(0)))= (rho)/(2ip a)`
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