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Question-39267




Question Number 39267 by ajfour last updated on 04/Jul/18
Commented by ajfour last updated on 04/Jul/18
Find electric field due to ring of  charge Q at P(x,y) in its plane.
FindelectricfieldduetoringofchargeQatP(x,y)initsplane.
Answered by ajfour last updated on 04/Jul/18
E^�  = ∮((dQ(r^� −R^� ))/(4πε_0 ∣r^� −R^� ∣^3 ))      =(Q/(4πε_0 (2π)))∮(((x−Rcos θ)i^� +(y−Rsin θ)j^� )/([(x−Rcos θ)^2 +(y−Rsin θ)^2 ]^(3/2) ))dθ   let  x= rcos φ,  y=rsin φ    E^�  = (Q/(8π^2 ε_0 ))[(∮(((rcos φ−Rcos θ)dθ)/([r^2 +R^2 −2rRcos (θ−φ)]^(3/2) )))i^�            +(∮(((rsin φ−Rsin θ)dθ)/([r^2 +R^2 −2rRcos (θ−φ)]^(3/2) )))j^�  ]   .....  please help..
E¯=dQ(r¯R¯)4πϵ0r¯R¯3=Q4πϵ0(2π)(xRcosθ)i^+(yRsinθ)j^[(xRcosθ)2+(yRsinθ)2]3/2dθletx=rcosϕ,y=rsinϕE¯=Q8π2ϵ0[((rcosϕRcosθ)dθ[r2+R22rRcos(θϕ)]3/2)i^+((rsinϕRsinθ)dθ[r2+R22rRcos(θϕ)]3/2)j^]..pleasehelp..

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