What Is the Electric Flux Through a Plane in the x-y Direction?

In summary, the problem involves finding the electric flux passing through a plane due to a linear charge lying on the y-z plane. The formula used is flux = (integral(integral)(Ds * dS)), and the answer is 1/8 of the given line charge. An analytical solution using the formula was also provided, resulting in a flux of 0.25 uC.
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Electrostatics Flux Problem

Homework Statement


A linear charge rho L = 2.0 uC lies on the y-z plane. Find the electric flux passing through the plane extending from 0 to 1.0m in the x direction and from -infinity to infinity in the y direction.


Homework Equations


Alright, so the formula to use is:

flux = (integral(integral)(Ds * dS)) where dS is a vector whose direction is normal to the surface element ds and has a magnitude of ds and Ds is the electric flux density passing through ds

Turns out the answer is simply 1/8 * the given line charge.

This is because the lines x = 0 and x = 1 when viewed from above make a 45 degree angle. The area enclosed here is exactly 1/8th of the entire area.

A more analytical solution would be great though.
 
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The Attempt at a SolutionA more analytical solution would be to use the formula above. Start off with the double integral of electric flux density over the given area and solve for the flux:Flux = (integral(integral)(Ds * dS)) = (integral(integral)(rho/epsilon_0) * dS) = (integral(integral)(2.0 uC/8.85e-12 C^2/Nm^2 ) * dS) = (1/8) * (2.0 uC) = 0.25 uC
 

FAQ: What Is the Electric Flux Through a Plane in the x-y Direction?

What is flux in electrostatics?

Flux in electrostatics refers to the amount of electric field passing through a given surface area. It is a measure of the electric field strength and is represented by the symbol Φ.

How is flux calculated in electrostatics?

Flux can be calculated by taking the dot product of the electric field vector and a vector representing the surface area. The formula for calculating flux is Φ = E * A * cos(θ), where E is the electric field, A is the surface area, and θ is the angle between the two vectors.

What are the units of flux in electrostatics?

The units of flux are N*m²/C or V*m, which can also be written as joules per coulomb (J/C).

How does the direction of the surface affect flux in electrostatics?

The direction of the surface does not affect the magnitude of flux, but it does affect the sign. If the surface is perpendicular to the electric field, the flux will be positive. If the surface is parallel to the electric field, the flux will be zero. And if the surface is at an angle to the electric field, the flux will be positive or negative depending on the direction of the electric field.

What is the significance of flux in electrostatics?

Flux is an important concept in electrostatics as it helps us understand the behavior of electric fields and their impact on charged particles. It is also used in the calculation of electric potential and capacitance, which are essential in many technological applications.

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