Gauss's Law For Magnetism Puns

I understand that the Gauss law for magnetism states that the divergence of magnetic fields is zero in all points, which denies the existence of magnetic monopoles. However, most derivations for this statements come from the Biot-Savart law, which describes magnetic fields generated by electric currents. If the Gauss law for magnetism comes from the Biot-Savart law, it appears to me that the statement that magnetic monopoles do not exist is only true when such field is generated by electric current, but it doesn't apply if the monopole was generated by a particle or anything other than electric current.

Basically, does the Gauss law for magnetism deny the existence of magnetic monopoles in general or only when the field is generated by some electric current?

Edit: thanks for your replies, as you said, sometimes we (especially undergrads) lose touch with the fact that these equations and plenty of other laws are rooted in empirical observation

Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with positive charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is:

A. Q/4(PI)(epsilon)R^2 B. Q/8(PI)(epsilon)R^2 C. Q/72(PI)(epsilon)R^2 D. 17Q/72(PI)(epsilon)R^2 E. none of these

How would you go about solving this question? I tried taking a Gaussian Surface that spans a radius of 2R and used the equation: kQr/R^3 but ended up with Q/64(PI)(epsilon)R^2 which is really close to C but not quite.

Any help would be really appreciated. My exam is next Wednesday.

Say I was given Hollow cylinder with inner radius A and Outer Radius B and charge q. At the axis of the cylinder is a long line of charge of magnitude q as well. How do I find the electric potential between a point A/2 and 5B? So I know you start by finding the Electric field and then integrate from A/2 to 5B. But where do I put my Gaussian surface to get the correct equation for the Electric Field?

I am trying to work this problem, but I cannot get the answers in my book's index

A spherical distribution of charge P = Po[1 - ( R^2 /b^2 )] exists in the region 0≤ R ≤ b . This charge distribution is concentrically surrounded by a conducting shell with inner radius Ri (> b) and ourter radius Ro. Determine E everywhere.

(P is supposed to be surface charge usually denoted by variable "rho", I could not create the variable on this keyboard so I used P)

I know the four cases would be:

0≤ R< b, b≤ R < Ri, Ri ≤ R < Ro, R > Ro

I am trying to use Gauss's law and symmetry properties, but I am not getting the correct answers. Any help you could provide is appreciated. Thank you!

All across sci-fi you hear of solid ferrous, tungsten or nickel alloy slugs being tossed out of magnetic weapons but not much else. It does make sense since explosive filler compounds won’t have the same magnetic properties leading to an unevenly magnetic projectile, the magnetic casing being flimsier due to be hollow, various advanced fuses with metallic parts perhaps not liking extreme magnetism, and so on. Yet, the High Explosive (HE) round is an integral part of a modern tank’s ready rack. Buildings, light vehicles, infantry fighting positions, gun emplacements, and other such soft targets that may just have a APFSDS round sail through without doing much are served with the blast of general purpose HE. Chances are high there are more soft targets than hard targets like IFVs or other tanks.

What would be a good substitute for the general purpose HE shell? My first guess would be some sort of canister shot, but that would lose effectiveness at mid to longer ranges among other drawbacks. Thoughts?

Imagine you have a conducting infinite plate with uniform charge density ¤. The electric field outside the plate is ¤/e. However, my textbook says if you have another infinite plate with an equal and opposite change density across from it, the electric field between the two is still ¤/e. Why does superposition not apply here. Would this change if they were non-conducting?

(sorry for not using the correct symbols, my keyboard doesn't have them)

Textbook pic

I read the following footnote from this book (pg 155):

> It turns out that when we have time-dependent currents and/or charges in motion, Newton’s third law may not hold for forces between charges and/or conductors. An essential consequence of the Newton’s third law in mechanics is conservation of momentum of an isolated system. This, however, holds even for the case of time-dependent situations with electromagnetic fields, provided the momentum carried by fields is also taken into account.

Could someone explain this to me?

Gauss's Law says there is electric field normal to the Gaussian surface for symmetric charge distributions. However, for an irregularly shaped conductor or a regularly shaped conductor with nonuniform surface charge, how can one say that the electric field is zero? Since the integral is no longer E*SA, isn't it possible that there is electric field, except the electric field is always tangential to the surface (inside the conductor)?

Both laws revolve around the idea that a loop or a surface that encloses some charge or current have a flux or line integral that only depends on what’s inside the loop. This makes no sense to me.

Consider Gauss’s law. Imagine an empty spherical surface and a charge right outside of it. Everyone says if the field lines from the outside charge penetrate the surface, they also leave the surface, so it cancels the original flux contribution. But isn’t the the field strength less as it leaves (field lines are really a bunch of discrete field vectors, which get smaller as you move away from the object). I’ve never ever seen a proper explanation for this. Can someone give me a geometric explanation or derivation of these laws?

edit, nevermind, I figured it out, it is the wire formula+ the loop formula

https://imgur.com/a/C3gZ1ST

So the problem says to find the magnetic field induced by the current in a circular loop (image 1). Usually that's just integrating biot-savard's formula from 0 to 2pi (image 2). The integration gives uo*I/2R

I got it wrong so many times the system gave the answer which is what you see in image 1

I have no idea how it got there so I searched the problem and this website has it. The problem is they split the biot savard into an addition and I have no idea where that came from (image 3).

Does anyone know why the website solved it that way? and why does it work?

Thanks for all of your help, I'll be on here a BUNCH, lol.

So I was studying for a Gauss's law. And when the E field and A vector are perpendicular then the integral becomes E * dA, instead of E dot dA because apparently E * dA = E dot dA when they are perpendicular.

But the thing is that the dot product of two perpindicular vectors = 0.

Cause a dot b = |a| * |b| * cos(θ). cos(90) = 0. so |a|*|b| * 0 = a dot b = 0

So where does E * da come from?

Thanks!

Over my many years of playing Skyrim, I've found that increasing my movement speed past 110-120% sends me flying off the tops of stairs and playing out micro-falls as I run over rugged terrain. Back in the LE days, I noticed it most prominently while riding Kyrkrim from Apocalypse, and more recently I've seen it while stacking speed buffs from Adamant and Thaumaturgy. Do any of y'all know of a mod that helps us keep our feet on the ground at high speeds?

I suppose the root of the problem is that in video games, our character doesn't ambulate by pushing against the ground with their feet - they behave like Newton's Cannonball fired level with the ground, with a constant horizontal velocity so long as the movement key is held. If the speed at which the descending slope of the ground falls away from under us is greater than how quickly we fall, then we end up in the air and Newton's Punch-Cat falls down the stairs.

Edit: I made a diagram.

Aim assist is one thing, it's already a little unfair, but to load their magazines with magnetic rounds too? Controller players get free ammo power-ups.

I fully understand the controller players are about to pull up and say aim assist isn't that helpful blah blah. It's is. I have friends on PC switching to controller because they get way more kills. I don't want to play on a controller, I bought a PC for a reason...

They need to fix this or change match making lobbies.