Note: you must start every problem with the general formulation of the Gauss law

Question

Note: you must start every problem with the general formulation of the Gauss law, choose the surface, reduce the general expression to the specific case described in the problem, and then integrate over the surface that you have chosen to calculate the flux.

10. A very large metallic dome has a form of a sphere with the radius R = 17 m, half of which is underground. During a thunderstorm, it accumulated an induced charge with the density = 120x10^-6 C/cm2. In addition, there is an electric field with the magnitude E1 = 120 N/C pointing vertically from the cloud above to the ground. A person stands next to the dome on the ground. What is the magnitude of the electric field at the person’s location?

Explanation / Answer

Given: dome has a form of sphere with radius , r = 17 m accumulated charge density , = 120x10-6 C/cm2                                                 = 120x10-6 C/cm2 (1 cm2 / 10-4 m2)                                                 = 120 x10-2 C/m2 additional electric field pointing from could above the ground is ,                                             E1= 120 N/C ___________________________________________________________ Solution: Consider ,general formulation of the Gauss law electric flux = E = E.dS = q /o                                      E (S) = q /o                                            E =  q /(S)o                                            E = q/(4r2)o                                            E = /o                                            E = q/(4r2)o                                            E = /o Here , q is the charge on the dome ,               S is the surface area of the sphere ,               ( = q/S ) is the charge density of the sphere               o is the permitivity of the free space ,8.854 x10-12 F/m Hence ,         magnitude of the electric field at the person’s location is ,                                        E ' = E + E1                                              = E1 + /o                                              = (120 N/C) + (120 x10-2 C/m2 )/(8.854 x10-12 F/m)                                              = 135531963074.59 N/C                                              (or)                                         E' = 13.5 x1010 N/C                                                              = E1 + /o                                              = (120 N/C) + (120 x10-2 C/m2 )/(8.854 x10-12 F/m)                                              = 135531963074.59 N/C                                              (or)                                         E' = 13.5 x1010 N/C                                                 (or)                                         E' = 13.5 x1010 N/C                

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