1sir i couldn,t understand th e potential difference b/w d 2 spheres...
how,s it k2q/r??
Two identical metallic balls of radius 2 m are placed in a homogenous poorly conducting medium with restivity 4 × 10^-3 m. The distance between them is much larger than their size. The resistance of medium between the balls is x × 10^-3 . Find the value of x.
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2 Answers
66If charges +q and &ndash q are placed on the two spheres, then the potential difference between then is
V=\dfrac{2q}{4\pi\epsilon_0 R}
R being the radius.
The field on the surface of each sphere is
E=\dfrac{q}{4\pi\epsilon_0 R^2}
Hence the current density (which is radial) is
j=\sigma E=\dfrac{\sigma q}{4\pi\epsilon_0 R^2}
with σ being the conductivity. So the total current leaving one sphere (and entering the other one) is
I =j \,4\pi R^2 =\dfrac{\sigma q}{\epsilon_0 }
Hence, the total resistance between the two conductors is
r=\dfrac{V}{I}=\dfrac{1}{2\pi\sigma R}=\dfrac{\rho}{2\pi R}
Plug in the values to get x=\pi ohms
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