Over-complicating physics concepts

[starstruck_]

I’m not sure what’s up but I find myself over complicating concepts that are new and ones that I was really good with and have been practicing for the last like 3 years.

I find myself trying to connect things to previous concepts but it isn’t working out.

I’m in second year but I’ve found myself asking stupid questions about first year concepts that I knew in and out-maybe I’m just being paranoid.

Like we had a lab yesterday and the lab manual gave the equation E=
-(grad)V

And then asked what happens to the negative sign.

Instead of going and immediately saying that it disappears because the electric field and potential point in opposite directions. I thought about the fact that the potential is the work done by the electric field and if you find the integral of the electric field with respect to r, the negative sign comes out.

This is where I am stuck, I know if the derivative is taken for the potential, it will become positive again.

So I don’t understand why the equation says
E=
-(grad)V

and I don’t understand how everyone already knows they point in opposite directions. Okay maybe the fact that a negative vector means opposite directions but how?? I have no intuition.I can’t even tell if the issues I’m having are me not grasping concepts at all, me overthinking, or if I’m actually asking good, legitimate questions.I also don’t understand a lot of what I used to understand.

I don’t know how we know that planets sweep put equal areas in equal amounts of time-
HOW do we know those areas are equal?

Where did Gm1m2/r^2 and it’s parallel electricity version come from

Why does force conceptually drop exponentially, over a distance??

I don’t understand anything!
I can’t even picture or imagine Physics problems anymore and when I do, I’m wrong.

I can’t figure things out on my own using previous concepts (like i used to) and sometimes I get confused with those previous concepts when I know for a fact I knew them inside out last year.I’m not sure what’s wrong, am I not using the right mindset for physics? Is this just normal, and there’s nothing wrong? Did I never understand stuff in the first place? Or I did understand and just forgot minor details?I don’t want to say that Physics isn’t for me because I absolutely love my major. I am drowning in work, there is something due everyday but it’s not a chore to me at all.

I’m not bright, in fact I am probably the dimmest out of the people in my year but I’m trying really hard to build an intuition as good as theirs.

 

[RPinPA]

I wouldn't call this "stupid". Your last sentence spells out your goal, and it's a really important one. To really understand physics deeply, I believe you have to know it in both your head and your "gut". You are trying to work toward that kind of deep understanding and that's a very good thing to do. You want to be able to understand what is going to happen and describe it before ever writing down an equation. When you know what's happening, then you can write down the relevant equations.

The alternative is to randomly throw equations at a problem just because they seem to have some of the right symbols, with no knowledge of how to choose the right ones.

OK, now let me try to address your questions (fixing the math notation. See the LaTeX primer link below for how to do that).

So I don’t understand why the equation says
$E= -\nabla V$

and I don’t understand how everyone already knows they point in opposite directions. Okay maybe the fact that a negative vector means opposite directions but how??

Yes, the negative of a vector is a vector of the same magnitude in exactly the opposite direction. I'm not sure what to add to that.

But as for the deeper meaning of the negative sign, for me it's "things roll downhill". Everything in nature wants to get to lower energy. If you have a way for a particle to get to a lower energy than it currently has, it's going to want to do that. I think of electric potential as an analog to height. Gradient has the mathematical property that it gives the direction of steepest ascent. So $-\nabla$ is the direction of steepest DESCENT. The most downhill direction. Things will want to fall that way.

The difference between gravity and electric force is that there are negative charges, but not negative mass. Negative charges will want to fall uphill. The force they feel is upward in potential. But we capture that idea by defining electric field as the force per unit charge. If the force on a negative charge is uphill, the field causing it is downhill.

Hope that clarifies something and helps your intuition.

I don’t know how we know that planets sweep put equal areas in equal amounts of time-
HOW do we know those areas are equal?

Where did $\frac {G m_1 m_2}{r^2}$ and it’s parallel electricity version come from?

The equal area law was observed experimentally by Kepler. Newton postulated the Law of Universal Gravitation that you quote, and showed that it leads to Kepler's Laws, including the Equal Area Law. It can be proven with Calculus. It turns out to be a reflection of the conservation of angular momentum. It's a restatement of that conservation law.

I believe Coulomb postulated the electrostatic version that bears his name.

There's an intuitive explanation. The area of a sphere of radius r is $4\pi r^2$, proportional to $r^2$. If you can imagine these forces being caused by some stuff, for instance some sort of particle, then that stuff is spread out over an area which grows as $r^2$ so the concentration falls off as $1/r^2$. Of course we know since Einstein that Newton's Law is only a really good approximation, not exactly true to the last decimal place in all circumstances. But we also know that space is not flat, that it's distorted by the presence of mass. I know little about General Relativity so I can't say much more about how Einstein modifies the $1/r^2$ law and whether a geometric explanation still holds.

Why does force conceptually drop exponentially, over a distance??

I don't know what you mean by that. Gravitational and electrostatic force (of a point charge) drop off as $1/r^2$ as I said. If you take an Electricity and Magnetism course you'll learn that dipoles (a positive and negative charge close together so their fields almost cancel out) give rise to $1/r^3$ forces. Magnets are dipole fields, so magnetic force is an inverse cube force.

The term "exponential" means proportional to $e^{-r}$, which is a much faster decay than $1/r^2$ or $1/r^3$.

I can’t even picture or imagine Physics problems anymore and when I do, I’m wrong.

You didn't give that impression here, but perhaps you could give an example. I think you're probably not far off, and you're just at a temporary obstacle on the way to rebuilding your understanding deeper and more thoroughly.

 

[Dr. Courtney]

The positive force is down the potential hill.

 

[robphy]

Recall the work-energy theorem, where the work done is equal to the change in kinetic energy.
The work can be split up into work done by conservative forces and work not done by conservative forces.
The minus sign in $\vec E=-\nabla V$ can be traced to the definition of the "change in potential energy" as minus the work done by conservative forces.
This allows us to write the "work not done by conservative forces" equals the change in total mechanical (kinetic+potential) energy.

Try to seek opportunities to teach, TA, or tutor.
A good way to learn something is having to teach it to someone else.

 

[Stephen Tashi]

I also don’t understand a lot of what I used to understand.

I don’t know how we know that planets sweep put equal areas in equal amounts of time-
HOW do we know those areas are equal?

It isn't clear what you mean. Here are two possibilities:

1) You once understood how we prove the areas are equal and have forgotten

2) You were comfortable with knowledge that planets sweep out equal areas within an ellipse, but are now worried about how to prove this.

Possibility 1) is a case of forgetting. Possibility 2) is a case of formulating questions and doubts.

As far a possibility 2) goes, advancing in a field of study typically goes along that way. We get comfortable with a topic. Then we, or someone else, raises a seemly simple question that baffles us. We are made uncomfortable with our understanding and study things in a more precise way. Of course, it's awkward if a lot of these disturbances happen all at one time.

Typically, more elementary courses in math and science convince students of the truth of many statements using intuition or the outright "voice of authority". This is because proving simple looking results in a precise logical manner requires a sophisticated and abstract understanding about how to reason. Later when students begin to develop sophisticated thinking, they must go back and reconsider the elementary material to sort things out.

 

[starstruck_]

Recall the work-energy theorem, where the work done is equal to the change in kinetic energy.
The work can be split up into work done by conservative forces and work not done by conservative forces.
The minus sign in $\vec E=-\nabla V$ can be traced to the definition of the "change in potential energy" as minus the work done by conservative forces.
This allows us to write the "work not done by conservative forces" equals the change in total mechanical (kinetic+potential) energy.

Try to seek opportunities to teach, TA, or tutor.
A good way to learn something is having to teach it to someone else.

I do want to TA! I wish I knew how it worked for my school. Thank you for the suggestion! Might try talking to my first year professor since I know him well and it’ll keep me in loop with the basics.

 

[starstruck_]

I wouldn't call this "stupid". Your last sentence spells out your goal, and it's a really important one. To really understand physics deeply, I believe you have to know it in both your head and your "gut". You are trying to work toward that kind of deep understanding and that's a very good thing to do. You want to be able to understand what is going to happen and describe it before ever writing down an equation.

Thank you! You’ve basically touched on everything I was having trouble clearing my thoughts for.

(Completely unrelated but
I think I’m probably just going through a heightened ocd period right now, since I over think a lot when it’s really bad.I’m trying my best to stop myself from wandering off to useless details.)

Thanks for clearing up everything for me! My questions were probably really stupid and odd to answer so I’m really grateful that you took the time to answer them so thoroughly!

 

[starstruck_]

It isn't clear what you mean. Here are two possibilities:

1) You once understood how we prove the areas are equal and have forgotten

2) You were comfortable with knowledge that planets sweep out equal areas within an ellipse, but are now worried about how to prove this.

Possibility 1) is a case of forgetting. Possibility 2) is a case of formulating questions and doubts.

As far a possibility 2) goes, advancing in a field of study typically goes along that way. We get comfortable with a topic. Then we, or someone else, raises a seemly simple question that baffles us. We are made uncomfortable with our understanding and study things in a more precise way. Of course, it's awkward if a lot of these disturbances happen all at one time.

Typically, more elementary courses in math and science convince students of the truth of many statements using intuition or the outright "voice of authority". This is because proving simple looking results in a precise logical manner requires a sophisticated and abstract understanding about how to reason. Later when students begin to develop sophisticated thinking, they must go back and reconsider the elementary material to sort things out.

Out of the possibilities it’s a mix of both- I never learned how to prove that the areas were equal but for something really basic, I did once understand but have forgotten now.

I’ve found I had a lot more questions about E&M this year - many about things we might not even get to learn till 4th year or further (at least what I was told by fellow students and my first year professor)This ^ is also feeding into my overthinking ://

 

[Klystron]

I find myself trying to connect things to previous concepts but it isn’t working out.

I’m in second year but I’ve found myself asking stupid questions about first year concepts that I knew...

I use two study techniques that help me understand concepts and "fix" new knowledge.

1. As part of preparing for the next math and science course in a series, I read my class notes and lab reports and skim the textbooks from the prior courses; perhaps even solving a few homework problems to refresh the concepts and applications required for subsequent learning.
2. When work load permits, I try to personally connect with science and math using outside reading and/or a good science video. My understanding of Kepler from first year Astronomy was enhanced after I watched a video ("Nova", "Connections"?) that dramatized how Tycho Brahe's observations and data informed Kepler's reasoning. Learning that Brahe was a brawler while Kepler sometimes supported his research writing popular horoscopes helped me relate to them as people and scientists. When I next encountered Kepler's laws in Calculus courses, it seemed like meeting an old friend.

During a break after second year I read an excellent book -- E.T. Bell's "Men of Mathematics" -- that led me to read books by the mathematicians described by Professor Bell. The OP can find more modern texts that help personalize concepts and connect with new material.

 

[RPinPA]

The positive force is down the potential hill.

Maybe we're stuck on a semantic point here.
$F = qE = -\nabla U = -q \nabla V$

Force is downhill in potential energy U. It's the negative gradient of U. As I said, everything wants to get to lower energy.
But downhill in energy U is uphill in potential V for a negative charge. Force on negative charges is uphill in electric potential (voltage). In terms of a battery for instance, an electron is going to want to go away from the - terminal and toward the + terminal. That is uphill in voltage.

 

[Zap]

It's work done per unit charge.