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An electric dipole is placed at a distance x from centre O on the axis of a charged ring of R and charge Q uniformly distributed over it. (a) Find the net force acting on the dipole. (b) What is the work done in rotating the dipole through 180^@? |
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Answer» `(DE)/(DX)=kQ[((R^2+x^2)^(3//2)-x.3/2(R^2+x^2)^(1//2)(2X))/((R^2+x^2)^3)]` or `(dE)/(dx)=kQ[(R^2+x^2-3x^2)/((R^2+x^2)^(5//2))]` or `dE=Q/(4piepsilon_0)[(R^2-2x^2)/((R^2+x^2)^(5//2))]dx` `:.|/_\E|=Q/(4piepsilon_0)[(R^2-2x^2)/((R^2+x^2)^(5//2))]/_\x` Her `/_\x=2a` `:. F=|q/_\E|=(Qqa)/(2piepsilon_0)[(R-2x^2)/((R^2+x^2)^(5//2))]` B. `W=U_f-U_i` `=-pEcos180^@+pEcos0^@=2pE` `2(q)(2a)[1/(4piepsilon_0 (Qx)/((R^2+x^2)^(3//2)))]` `=(aqQx)/(piepsilon(R^2+x^2)^(3//2)` |
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