2- consider a metalic sphere of the raduis R=3 metre placed in a vacuem . the ma

Question

2- consider a metalic sphere of the raduis R=3 metre placed in a vacuem . the magnitude of the electric field of the distance r= 5 metre away from the centre of the sphere is 21.6 Volts /metre

a) what is the the net flux of the electric field through the spherical Gassuian surface that has raduis

r= 5 metre ? the centre of the gaussian surface coincides with the centre of the metalic sphere

b) what is the total charge Q located at the surface of the metalic sphere ?

c) calculate the magnitiude of the electric field in vacuem just above the surface of the metalic sphere

Explanation / Answer

phi=int(E dA) The Gaussian sphere area-vector is parallel to E-vector everywhere, thus int(E dA)=EA phi=EA=E*4*pi*R^2=(21.6 V/m)*(4*pi*25 m^2)=6785.8 V*m E for a point charge (or outside a solid or empty charged sphere/shell) = kQ/R^2 21.6 V/m=(1/4/pi/e0)*(Q)/25 m^2 Q=6.00*10^-8 C = 0.06 uC E=kQ/R^2=(1/4/pi/e0)*(6*10^-8)/(9) for R=3m E= 59.95 V/m

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