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704_Physics ProblemsTechnical Physics

704_Physics ProblemsTechnical Physics - 44 Gausss...

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44 Gauss’s Law *P24.59 The vertical velocity component of the moving charge increases according to m dv dt F y y = m dv dx dx dt qE y y = . Now dx dt v x = has the nearly constant value v . So dv q mv E dx y y = v dv q mv E dx y y v y y = = z z −∞ 0 . v x v y x y d q v 0 θ Q FIG. P24.59 The radially outward compnent of the electric field varies along the x axis, but is described by E dA E d dx Q y y −∞ −∞ z z = = 2 0 π b g . So E dx Q d y −∞ z = 2 0 π and v qQ mv d y = 2 0 π . The angle of deflection is described by tan θ π = = v v qQ dmv y 2 0 2 θ π = tan 1 0 2 2 qQ dmv . P24.60 First, consider the field at distance r R < from the center of a uniform sphere of positive charge Q e = + b g with radius R . 4 2 0 0 4 3 3 4 3 3 0 π ρ π π r E q V e R r e j = = = + F H G I K J in so E e R = F H G I K J 4 0 3 π r directed outward (a) The force exerted on a point charge q e = − located at distance r from the center is then
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