1. Tardigrade
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  3. Physics
  4. A flat, square surface with sides of length L is described by the equations x = L, 0 le y le L,0 le z le L The electric flux through the square due to a positive point charge q located at the origin (x = 0, y = 0, z = 0) is (q/Nε0) Find the value of N?

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Q. A flat, square surface with sides of length $L$ is described by the equations
$x = L, 0 \le y \le L,0\le z \le L$
The electric flux through the square due to a positive point charge $q$ located at the origin $(x = 0, y = 0, z = 0)$ is $\frac{q}{N\varepsilon_0}$ Find the value of $N$?

Electrostatic Potential and Capacitance

Solution:

image
Imagine a charge $q$ at the center of a cube of edge length $2L$ (figure). Then $\phi = q/\varepsilon_0$
Here, the square is $1/24$ of the surface area of the imaginary cube, so it intercepts $1/24$ of the flux. That is.
$\Phi = \frac{q}{24\varepsilon_0}$