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#1 Posted 01:33am 06-03-10 resistance..!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 Posted 02:39am 06-03-10 Re: resistance..!If charges +q and &ndash q are placed on the two spheres, then the potential difference between then is [im]http://codecogs.izyba.com/gif.latex?V%3D%5Cdfrac%7B2q%7D%7B4%5Cpi%5Cepsilon_0%20R%7D[/im] R being the radius. The field on the surface of each sphere is [im]http://codecogs.izyba.com/gif.latex?E%3D%5Cdfrac%7Bq%7D%7B4%5Cpi%5Cepsilon_0%20R%5E2%7D[/im] Hence the current density (which is radial) is [im]http://codecogs.izyba.com/gif.latex?j%3D%5Csigma%20E%3D%5Cdfrac%7B%5Csigma%20q%7D%7B4%5Cpi%5Cepsilon_0%20R%5E2%7D[/im] with σ being the conductivity. So the total current leaving one sphere (and entering the other one) is [im]http://codecogs.izyba.com/gif.latex?I%20%3Dj%20%5C%2C4%5Cpi%20R%5E2%20%3D%5Cdfrac%7B%5Csigma%20q%7D%7B%5Cepsilon_0%20%7D[/im] Hence, the total resistance between the two conductors is [im]http://codecogs.izyba.com/gif.latex?r%3D%5Cdfrac%7BV%7D%7BI%7D%3D%5Cdfrac%7B1%7D%7B2%5Cpi%5Csigma%20R%7D%3D%5Cdfrac%7B%5Crho%7D%7B2%5Cpi%20R%7D[/im] Plug in the values to get [im]http://codecogs.izyba.com/gif.latex?x%3D%5Cpi[/im] ohms |
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#3 Posted 2:32pm 06-03-10 Re: resistance..!sir i couldn,t understand th e potential difference b/w d 2 spheres... how,s it k2q/r?? |
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