Respuesta :
- The charge per unit length (in C/m) exists on the copper rod is [tex]1.78\times10^{-11}\rm C/m[/tex]
- The electric flux through a cube of side 3 cm situated such that the rod passes through opposite sides of the cube perpendicularly is [tex]1.48\times10^{-3}\rm N-m^2/C[/tex].
What is electric flux?
The number of electric lines or force that intersects a given area is called the electric flux.
Given information-
Radius of copper rod is 2 cm.
The electric field strength on the copper rod is 4 N/C.
The electric field at 4 cm from the center of a long copper rod.
- (a) The charge per unit length (in C/m) exists on the copper rod.
The electric charge can be given as,
[tex]q=\dfrac{4Er^2}{k}[/tex]
Put the values,
[tex]q=\dfrac{4\times4\times(0.02)^2}{8.988\times10^9}\\q=7.12\times10^{-13}[/tex]
The charge per unit length is,
[tex]\lambda=\dfrac{q}{l} \\\lambda=\dfrac{7.12\times10^{-13}}{0.04} \\\lambda=1.78\times10^{-11}[/tex]
Thus, The charge per unit length (in C/m) exists on the copper rod is [tex]1.78\times10^{-11}\rm C/m[/tex]
- (b) The electric flux through a cube of side 3 cm situated such that the rod passes through opposite sides of the cube perpendicularly.
By the Gauss's law the formula for the electric flux ,
[tex]\phi_e=\dfrac{q}{6a^2\times\varepsilon_0}\\[/tex]
Put the values,
[tex]\phi_e=\dfrac{7.12\times10^{-13}}{6\times3^2\times8.85\times10^{-12}}\\\phi_e=1.48\times10^{-3}[/tex]
Hence the The electric flux through a cube of side 3 cm situated such that the rod passes through opposite sides of the cube perpendicularly is [tex]1.48\times10^{-3}\rm N-m^2/C[/tex].
Hence,
- The charge per unit length (in C/m) exists on the copper rod is [tex]1.78\times10^{-11}\rm C/m[/tex]
- The electric flux through a cube of side 3 cm situated such that the rod passes through opposite sides of the cube perpendicularly is [tex]1.48\times10^{-3}\rm N-m^2/C[/tex].
Learn more about the electric flux here;
https://brainly.com/question/14372859
