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Obtain the expression of electric field at any point by continuous distribution of charge on a volume. |
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Answer» Solution :Suppose a continuous charge DISTRIBUTION in space has a charge density `rho`. Choose any convenient origin O and let the position vector of any point in the charge distribution be `vecr`.  Divide the charge distribution into small volume elements of size `DeltaV`. The charge in a volume element `DeltaV` is `rhoDeltaV`. Now, CONSIDER any general point P (inside or outside the distribution with position vector `vecR`. Electric field due to the charge `rhoDeltaV`is given by Coulomb.s LAW. `vecE = sum(krhoDeltaV)/(r.)^(2).hatr` where r. is the distance between the charge element and P and f. is a unit vector in the direction from the charge element to P. By the superposition principle, the total electric field, `vecE = int_(V) (krho.DeltaV)/(r.)^(2)hatr = k -= (rho DeltaV)/(r^(2)).hatr` OR `vecE = kint(rho.DeltaV)/(r^(-2).hatr` In short, using Coulomb.s law and the superposition principle, electric field can be DETERMINED for any charge distribution, discrete or continuous or part discrete and part continuous. |
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