InterviewSolution
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InterviewSolution
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Obtain Gauss law from Coulomb 's law . |
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Answer» Solution :Gauss lawstates that if a charge Q is enclosed by an arbitrary closed surface then the TOTAL electric flux `Phi_(E)` through the closed surface is `Phi_(E)oint vecE.dvecA= (Q_("end"))/(epsilon_(0))` A positive point charge Q is surrounded by an imaginary sphere of radius r as shown in FIGURE. We can calculate the total electric flux through the closed surface of the sphere using the equation .  `Phi_(E)=ointvecE .dvecA= oint EdAcos theta ` The electric field of the point charge is DIRECTED radially outward at all point on the surface of the sphere . Therefore the direction of the area element `dvecA` is along the electric field `vecE` and `theta= 0^(@)` . `Phi_(E)=oint EdA ` since cos `0^(@)=1 ` E is uniform on the surface of the sphere `Phi_(E) = Eoint dA` Substituting for `oint dA = 4pir^(2)` and E `= (1)/(4piepsilon_(0))Q ` in equation 3 we GET `Phi_(E)= (1)/(4piepsilon_(0))(q)/(r^(2))xx4pir^(2)= 4pi(1)/(4piepsilon_(0))= (Q)/(epsilon_(0))` The equation (4) is called as Gauss.s law . The remarkable point about this result is that the equation ( 4) is equally true for any arbitrary shaped which encloses the charge Q. |
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