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Find Out an expression for electric intensity at any point due to an electric dipole. |
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Answer» Consider the an electric dipole of charges +q and −q separated by distance 2a with center at O. Goal : To find electric field at point P on the axial line of the dipole, OP = r. Let E1 and E2 be electric field on P due to charges +q and −q respectively. E1 = \(\frac{kq}{(r-a)^2}\) along BP E2 = \(\frac{kq}{(r+a)^2}\) along BP The resultant electric field at P, E = E1 - E2 (as both E1 and E2 are in opposite direction) E = \(\frac{kq}{(r-a)^2}\) - \(\frac{kq}{(r+a)^2}\) = kq \(\frac{4ra}{(r^2-a^2)^2}\) Define, p = 2aq E = k \(\frac{2pr}{(r^2-a^2)^2}\) If r >> a, then E = k \(\frac{2pr}{r^4}\) = k \(\frac{2p}{r^3}\) In vector form, \(\vec E\) = k \(\frac{2\vec p}{r^3}.\) |
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