Calculating Electric Flux on Hemispherical Surface | Gauss' Law Solution

In summary, using Gauss' Law, the electric flux through the hemispherical surface will be zero for both cases, since the electric field is perpendicular to the surface. This is because the dot product of ihat and khat is zero, meaning there is no component of the electric field in the direction of the surface. Therefore, the net field lines entering the surface will be the same as the lines coming out, resulting in a flux of zero.
  • #1
uchicago2012
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Homework Statement


(a) Calculate the electric flux through the hemispherical surface shown in the figure. (The surface is an open shell, with no bottom.) The electric field is uniform: E = E0 khat.
(b) If the electric field is instead E = E0 ihat, what is the flux?

Homework Equations


Gauss' Law

The Attempt at a Solution


I was just wondering, for b), since ihat dot khat = 0, does that mean the electric flux is zero? Because it seems like the electric flux will always be perpendicular to the normal force if it is E = E0 khat
 

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  • #2
the net field lines entering the surface are sae as not lines coming out so yes flux will be 0
 

FAQ: Calculating Electric Flux on Hemispherical Surface | Gauss' Law Solution

1.

What is electric flux and why is it important in calculating electric fields?

Electric flux is a measure of the electric field passing through a surface. It is important because it helps us understand the strength and direction of the electric field, which is crucial in many applications such as circuit design and electromagnetic wave propagation.

2.

How do you calculate electric flux on a hemispherical surface?

To calculate electric flux on a hemispherical surface, we use Gauss' Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. We can then use this formula to find the electric flux on the hemispherical surface by considering the charge enclosed by the hemisphere.

3.

Can the electric flux on a hemispherical surface be negative?

Yes, the electric flux on a hemispherical surface can be negative. This can occur if the electric field is directed in the opposite direction of the surface normal, which means the flux is leaving the surface instead of entering it.

4.

What are the units of electric flux?

The units of electric flux are newton-meters squared per coulomb (N·m^2/C). This is equivalent to volts per meter (V/m), which is the unit for electric field strength.

5.

What are some real-world applications of calculating electric flux on a hemispherical surface?

Some real-world applications include designing antenna systems, analyzing electric fields in capacitors, and studying the propagation of electromagnetic waves. It is also important for understanding the behavior of charged particles in electric fields, which is relevant in fields such as particle physics and plasma physics.

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