Questions tagged [gauss-law]

A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.

A law in Classical Electromagnetism and Newtonian Gravity.

Understanding Gauss's law

Classical Electromagnetism

Classical Electricity

Gauss's law for Electricity states that:

$$\nabla\cdot\vec E=\frac{q}{\epsilon_0}$$

Classical Magnetism

Gauss's law for Magnetism states that:

$$\nabla\cdot\vec B=0$$

Newtonian Gravity

Gauss's law for Gravity is simply Poisson's equation

$$\nabla\cdot\vec E=4\pi G\rho$$

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Electric flux through finite width/ infinitely long plane due to a point charge

The question is as follows: Consider a point charge Q placed at $(0,h,0)$ (Cartesian coordinates). Find the flux in an area formed by $y=0$, $z\leq0$, $x\geq l$ and $x\leq a$ $( l\leq x\leq a )$. I tried this by considering the two extreme lines…
AGV121
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Intuition behind defining divergence as flux divided by volume?

For a continuously differentiable vector field $F$ the divergence theorem can be used to give $$(\nabla\cdot F)(a) = \lim_{r\to 0} \frac{3}{4\pi r^3}\int_{|x-a|=r} F \cdot n dA$$ This should mean that for $c<3 $ $$\lim_{r\to 0} \frac{3}{4\pi…
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Electric field of a uniformly charged hollow cone using Gauss' Law

Suppose we have a uniformly charged hollow cone(ice cup) of surface charge density σ, slant height L and the half-angle at the vertex is θ. I want to calculate the electric field at its tip using Gauss law. I have done the calculation using…
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When to use Gauss's Law

What is the use of this equation and Gauss's Law As an example, for this problem I was able to to use the equation to have the exact same result without the use of Gauss's law as in the answer. However, for the same problem but for a charge inside…
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Charges lying on a Gaussian Surface

Let's say you have a spherical charge distribution of radius R. This distribution has some charge density as a function of radius. I know that I can determine the electric field outside of the charge density by forming a spherical gaussian surface…
zephyr
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Net Electric field on a Gaussian surface

While applying Gauss' Law, the electric field at a point on the Gaussian surface has to come from superposition of electric fields of all the charges, whether outside or inside the Gaussian surface. However, the charge $Q$ has to be only from inside…
Rew
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Conceptual question on Gauss's Law

By my understanding, the electric field in the surface integral expression for Gauss's Law represents the total electric field and any point on a closed Gaussian surface. However, when we employ Gauss's Law to find the electric field within a…
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Gaussian surfaces and Gauss law

Does Gauss law holds for any closed surface or it only holds for only Gaussian surface. Are every closed surface a Gaussian surface?
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If the electric field inside an infinitely long charged cylinder is non-zero except origin, how can be the inward flux zero?

If the electric field inside an infinitely long charged cylinder is non-zero except origin, how can be the inward flux zero? https://www.youtube.com/watch?v=BF3wEV4tWq8 If we look at this video, we would see that a charged ring has a non-zero…
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Calculating the magnetic flux at a certain location

I am currently preparing for a physics exam and I have troubles solving the question below a certain location in the southern hemisphere, Earth's magnetic field has a magnitude of 42 microTesla and points upward at 57° to the vertical. calculate…
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Why does a charge distribution with cylindrical symmetry have to be infinitely long?

Why does a charge distribution with cylindrical symmetry have to be infinitely long when applying Gauss's law? It seems unnecessary especially since the electric field emits radially.
Anna
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When I need to calculate the electric field due to a charged infinite plate, does the intensity of the field not drop with distance from the plate?

As opposed to calculating electric field due to a cylindrical wire or sphere where there is a dependence of the field to the distance between the point chosen and the charged body in itself. But in case of the charged plate, why do we not chose a…
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Gauss's Law with Moving Charges

My text claims that Gauss's Law has been proven to work for moving charges experimentally, is there a non-experimental way to verify this?
user24082
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Electric Flux vs Magnetic Flux Units

If electric flux is the number of electric field lines through a surface area and magnetic flux is a number of magnetic field lines through a surface area, why are the units for them different? Electric Flux: Magnetic Flux: Mathematically, I know…
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electric field inside a hollow ball and the Gauss's law

I am wondering about the answer to the PSE question here: Electric Field inside a hollow ball, excentred of a homogeneous charged ball I understand the solution, but I don't understand how it corresponds to the Gauss's law. The charge inside the…
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