44 Gauss’s Law*P24.59The vertical velocity component of the moving chargeincreases according tomdvdtFyy=mdvdxdxdtqEyy=.Now dxdtvx=has the nearly constant value v. SodvqmvE dxyy=vdvqmvE dxyyvyy==zz−∞∞0.vxvyxydqv0θQ FIG. P24.59The radially outward compnent of the electric field varies along the xaxis, but is described byE dAEd dxQyy−∞∞−∞∞zz==∈20πbg.So E dxQdy−∞∞z=∈20πand vqQmvdy=∈20π. The angle of deflection is described bytanθπ==∈vvqQdmvy202θπ=∈−tan1022qQdmv.P24.60First, consider the field at distance rR<from the center of a uniform sphere of positive chargeQe= +bgwith radius R.42004334330πρππrEqVeRrej=∈=∈=+FHGIKJ∈inso EeR=∈FHGIKJ403πr directed outward(a)The force exerted on a point charge qe= −located at distance rfrom the center is then
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