Question

A point charge q1 = 3.65 nC is located on the x-axis at x = 2.30 m , and a second point charge q2= -6.10 nC is on the y-axis at y = 1.30 m.

(a) What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r1 = 0.435 m ?

(b) What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r2 = 1.65 m ?

(c) What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r3 = 2.45 m ?

Answer 1

Flux through a closed surface is proportional to the amount of charge that is enclosed by the surface. i.e.,
  
a)
So, for a spherical surface of radius r1 = 0.435 m, there is no charge enclosed by the surface. So,
q_{enclosed} = 0. So,
  
b)
   For a spherical surface of radius r2 = 1.65 m, ther charge enclosed by the surface is,
q_{enclosed} = q2= -6.10 nC. So,
  
c)
  For a spherical surface of radius r3 = 2.45 m, ther charge enclosed by the surface is,
q_{enclosed} = q1+q2=3.65 - 6.10 = - 2.45 nC. So,