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Tushar Watts Grade: 12
        

A point charge q is placed at origin. Calculate the electric flux through the open hemispherical surface : (x-a) 2 + y2 +z 2 = a2 ,  x ≥ a.

7 years ago

Answers : (1)

Pratham Ashish
17 Points
										

Ø4589-1424_4788_8.bmp


electri flux trough the hemisphere will be same as through the circular surface at its mouth , coz they shere same field lines


flux through the circular surface ,


 consider a thin circular strip of width dr at a distance r from the centre


dØ = E. dA


     = q /4¶ε (a^2 + r ^2 )  . 2¶r dr  cosθ


     = -q r ( a/ √ a^2 + r^2 ) / 2  ε (a^2 + r ^2 )              { cosθ  = - a/ √ a^2 + r^2}


     =- (q /2ε ) ar / ( a^2 + r^2 ) ^3/2  dr


Φ   = -∫ (q /2ε ) ar / ( a^2 + r^2 ) ^3/2  dr


       = (q /2ε ) a / √ a^2 + r^2  ]


       =  - (q /2ε )  (  1 - 1/√2  ) 


flux through hemisphere  = - Φ


                                     =   (q /2ε )  (  1 - 1/√2  )    


 


 

7 years ago
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