[latex]E_x= intlimits _ Q frac{k}{R^2}cdot-cosphi , dq = intlimits^{2pi}_0 {frac{k}{R^2} frac{q}{alpha}cdot-cosphi } , dphi = \ intlimits^ frac{pi}{2}_0 {frac{k}{R^2} frac{-Q}{ frac{pi}{2} }cdot-cosphi } , dphi + intlimits^ {2pi}_ frac{pi}{2} {frac{k}{R^2} frac{Q}{ frac{3pi}{2} }cdot-cosphi } , dphi =\ frac{2kQ}{pi R^2}(sin frac{pi}{2} -sin 0 ) - frac{2kQ}{3pi R^2}(sin 2pi -sin frac{pi}{2} ) =\ frac{2kQ}{3pi R^2}(3-0-0+1)=frac{8kQ}{3pi R^2} \[/latex] [latex]E_y= intlimits _ Q frac{k}{R^2}cdot-sinphi , dq = intlimits^{2pi}_0 {frac{k}{R^2} frac{q}{alpha}cdot-sinphi } , dphi = \ intlimits^ frac{pi}{2}_0 {frac{k}{R^2} frac{-Q}{ frac{pi}{2} }cdot-sinphi } , dphi + intlimits^ {2pi}_ frac{pi}{2} {frac{k}{R^2} frac{Q}{ frac{3pi}{2} }cdot-sinphi } , dphi =\ frac{-2kQ}{pi R^2}(cos frac{pi}{2} -cos 0 ) + frac{2kQ}{3pi R^2}(cos 2pi -cos frac{pi}{2} ) =\ frac{2kQ}{3pi R^2}(0+3+1-0)=frac{8kQ}{3pi R^2} \[/latex]
