Question

A point charge q1q1q_1 = 4.10 nCnC is located on the x-axis at xxx = 2.15 mm , and a second point charge q2q2q_2 = -6.85 nCnC is on the y-axis at yyy = 1.30 mm .

a)What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r2r2r_2 = 1.50 mm ?

b)What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r3r3r_3 = 2.50 mm ?

Answer 1

part A)

using Gauss' law
The total electric flux through the sperical surface with radius r2 = 1.50 m ,

phi_E = Qin/epsilon

= q2/epsilon (since Qin = q2)

= -6.85*10^-9/(8.854*10^-12)

= -774 N.m^2/C <<<<<<<<-------------Answer

part B)

The total electric flux through the sperical surface with radius r3 = 2.50 m ,

phi_E = Qin/epsilon

= (q1 + q2)/epsilon (since Qin = q1 + q2)

= (4.1*10^-9 - 6.85*10^-9)/(8.854*10^-12)

= -310 N.m^2/C <<<<<<<<-------------Answer

we have solved this problem using Gauss' law.
Gauss' law: The net elctric flux through any closed surafec is equal to i/epsilon times of the charge enclosed by the closed surface.