# Fields and Forces

## Main Question or Discussion Point

I apologize in advance if this is supposed to go in the homework section, but this is not homework, it is just my inability to grasp the topic no matter what textbook I read.

So, here is my question. I have been taught 4 formulas for "Fields and Forces"

$$F = \frac{GMm}{r^{2}}$$

$$F = \frac{kq_{1}q_{2}}{r^{2}}$$

$$g = \frac{GM}{r^{2}}$$

$$E = \frac{kq}{r^{2}}$$

And 6 formulas for "Motion in Fields"

$$\Delta V = \frac{\Delta E_{p}}{m}$$ & equivalent for q instead of m

$$V = - \frac{GM}{r}$$ & positive equivalent for q where G = k and k = $$\frac{1}{4 \pi \epsilon _{0} r}$$

$$g = - \frac{\Delta V}{\Delta r}$$ & equivalent for E but instead of $$\Delta r$$ it gives me $$\Delta x$$

Now I'm sorry if I just fired 7 formulas at you guys and expected you to explain them, I know what they do, its just that their symbols confuse me, which is which? and especially when to use r^2 and when to use the formula without the r^2 on the bottom.

Again sorry, but if anyone would take the time to explain the formulas in practical terms, I would be eternally grateful, seriously.

Alternatively, if anyone knows any good online resource, a link would be great! (I already tried to google it, but results were vague and poorly explained)

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F=GmM/r^2 is the gravitational force between to bodies G being the gravitational constant and M m being the masses of the bodies , and this is an inverse square law
meaning the gravitational force is proportional to 1/r^2 so if we double the distance we quarter the force 1/2^2 . and the second one below that looks the be the electrical force also an inverse square law.

Thanks :D

Now I got 2 down. So when there is a gravitational FORCE, we use an inverse SQUARE law. OK.

Anyone got any other explanations for the other ones? I was told that the formulas were force, field, potential and energy...which is which? :S

hmmm.....let's see what i can do...
static electric forces and gravitational forces have alot in common.
starting with the force equation..
understating it is fairly simple, it is formula for magnitude of force at distance r, from a point mass/charge.
next comes understanding its direction,
gravity always attracts, so direction of force is opposite to distance vector (i hope u know force is a vector) so an extra minus sign is needed
attraction -> -ve sign repulsion -> +ve sign

Next is much more conceptual topic, FIELDS..
it so happened that physicist were unable to explain things like action at a distance, like how earth exerts a force(pulls) the moon without touching it.
(i'm using electricity but same applies for gravity as well)

So they said that every charge created what is called as a field around, and it is this field that exerts the required force on the charge. the field is given by the respective formula (it is a vector too) and its direction is given by where a POSITIVE charge experiences force...it can be said to be numerically equal to force on a unit +ve charge (consider direction also)

like place a charge in space n see where it goes, that gives direction of field

E = F / q and g = F / m

(HENCE, FIELD IF FORCE PER UNIT CHARGE/MASS)

Next comes a very important and slightly misunderstood concept, the potential and the potential energy.
(i suppose you know what a conservative force is)
Now,
Potential energy of a conservative force is not defined at all, all that is defined is CHANGE in the Potential Energy.

Let's say you have a large charge Q (or mass M for gravity) and you have another charge 'q' and you have to move the charge 'q' from point A to point B

The change in potential energy between two points (locations) say A & B (FOR A CONSERVATIVE FORCE ONLY) is defined as the work done BY YOU (external) agent in bringing the required charge/mass from A to B verrrrry slowly (quasi statically in technical terms) so that you don't lose energy as kinetic energy.

To calculate that u need to know integration, take any standard book, they must have done it..

U(B)-U(A)=Work done BY YOU

if they have given some formula in integral form, take a closer look, it is nothing but work done .. i.e Force X small displacement

Also, in almost every book, they take (they should take) potential energy at infinity as zero.
Actually the beauty in potential energy equation is that you can assume any point as zero potential. But if you take infinity as zero potential, the formula looks better

Next comes potential, V, or rather change in potential..
it is nothing but potential energy change per unit charge
V = U / q

Potential is to Potential Energy what Field is to Force...

that's all you need to know in electrostatics, gravity about fields and forces. Other things are just ways to calculate them, you will see that every formula you encounter (like gauss' law) is nothing but just a way u calculate these four things.
All complicated formulas have these underlying principles, look for them in the derivations, they are usually disguised.

Rest all you try to understand, if you ask everything, you will find physics boring.

With respect to your last question as to when to apply the formula, the answer is that depends. Practice is required for that. Every formula has a place, a use, it makes some complicated situation look easier. You have to practice, no other option

Here is a hint, If ever, something related to velocity is asked , try using the energy equations (Like conservation of energy)

Thank you so much!

Finally its much clearer to me :) I really appreciate the time you took to explain all that!