Question

A point charge q1q1q_1 = 4.35 nCnC is located on the x-axis at xxx = 2.10 mm , and a second point charge q2q2q_2 = -6.25 nCnC is on the y-axis at yyy = 1.00 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 r1r1r_1 = 0.385 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 r2r2r_2 = 1.50 mm ?

c)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 = 2.80 mm ?

Answer 1

Electric flux is given by:

= Vacuum permittivity = 8.854*10^-12

Q_net = net charge inside the gaussian spherical surface

Given that: q1 = 4.35 nC located at x1 = 2.10 m

q2 = -6.25 nC located at x2 = 1.00 m

Part 1.

When radius of gaussian surface is r = 0.385 m, So in this case

r < x1 & r < x2

So net charge inside the sphere will be zero, So

electric flux in this case will be:

= 0/(8.854*10^-12) = 0 N.m^2/C

Part 2.

When radius of gaussian surface is r = 1.50 m, So in this case

r < x1 & r > x2

So net charge inside the sphere will be:

Q_net = q2 = -6.25 nC = -6.25*10^-9 C

electric flux in this case will be:

= -6.25*10^-9/(8.854*10^-12)

= -705.896 N.m^2/C = -706 N/m^2/C

Part 3.

When radius of gaussian surface is r = 2.80 m, So in this case

r > x1 & r > x2

So net charge inside the sphere will be:

Q_net = q1 + q2 = 4.35 nC - 6.25 nC = -1.90*10^-9 C

electric flux in this case will be:

= -1.90*10^-9/(8.854*10^-12)

= -214.592 N.m^2/C = -215 N/m^2/C

Let me know if you've any query.