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Show that the tangential component of electrostatic field is continuous from one side of charged surface to another. [Hint : use the fact that work done by electrostatic field on a closed – loop is zero.] |
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Answer» Solution :The tangential component of electrostatic FIELD is continuous from one side of a charged surface to another, we USE that the work done by electrostatic field on a closed – loop is zero. Let ABA be a charged surface in the field of a point charge q lying at origin. Let`r_A andr_B` be its positive vectors at points A and B RESPECTIVELY. Let E be electric field at point P, thus Eis the tangential component of electric field E. `therefore E.dl=(E cos theta) dl` To prove that Eis continuous from one to another side of the charge surface, we have to find the value of`int _(ABA) E.dl` If it comes to be zero then we say that tangential component of E is continuous ` therefore int_A ^B E.dl=1/(4 pi e_0) q.(1/r_A-1/r_B) and int _B ^A E.dl =1/(4 pi e_0) q. (1/r_B-1/r_A)` `int _(ABA) E.dl =int _A ^B E.dl+ int _B ^ A E.dl=1/(4 pi e_0).q. (1/r_A-1/r_B+1/r_B-1/r_A)=0` HENCE PROVED |
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