Question

A continuous distribution of linear charge exists along the entire length of the y-axis, and has a uniform linear charge density of λ = 45.0 pC/m = 45.0✕10^-12 C/m.

What is the net electric flux through the surface of a sphere of radius r = 3.20 m, if it is located at the following positions?

ε_o = 8.854✕10^-12 C²/(Nm²)

(A) The sphere is centered on the origin.
Φ_E =_____ Nm²/C

(B) The sphere is centered on the point x = 4.00 m on the positive x-axis.
Φ_E =________ Nm²/C

Answer 1

A)

The length of the linear charge inside the sphere = 2*r

Charge enclosed by the sphere, Qin = lamda*2*r

= 45*10^-12*2*3.2

= 2.88*10^-10 C

the flus through the sphere, ΦE = Qin/epsilon

= 2.88*10^-10/(8.854*10^-12)

= 32.5 N.m^2/C <<<<<<<<--------------Answer

B) The length of the linear charge inside the sphere = 0

Charge enclosed by the sphere, Qin = 0

so, the flus through the sphere, ΦE = Qin/epsilon

= 0 N.m^2/C   <<<<<<<<--------------Answer