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An electric field is given E=a(xi+yj)/(x^2+y^2) where i and j are the unit vectors and a is a constant .A sphere with radius R is placed with its centre at the origin of the coordinate system.What is the electric flux through the sphere?

An electric field is given E=a(xi+yj)/(x^2+y^2) where i and j are the unit vectors and a is a constant .A sphere with radius R is placed with its centre at the origin of the coordinate system.What is the electric flux through the sphere?

Grade:12

1 Answers

Vikas TU
14149 Points
6 years ago
Flux =  Integeration of (E.ds)
where ds = area with unit vector that is => (xi + yj + zk)/root(x^2 + y^2 +z^2)
flux = a(xi+yj)/(x^2+y^2) *  (xi + yj + zk)/root(x^2 + y^2 +z^2) * ds
      = a(x^2 + y^)/(x^2 + y^2) * ds/root(x^2 + y^2 +z^2) 
      = a ds/root(x^2 + y^2 + z^2) 
       = (a/R) ds
       = (a/R) * 4piR^2
       = 4*pi*a*R

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