# Fundamental rules for physics mathematical derivations.?

• Mathematica
In summary, the conversation discusses a problem in calculating the force on a current carrying wire in the presence of a magnetic field. It is suggested to start with the most basic principles in physics, such as Newton's laws or Maxwell's equations, when approaching a new problem. The key is to practice solving problems in order to fully understand the concepts. The conversation also mentions the use of the Lorentz force and the relationship between electrical current, the number of electrons, and their speed. The importance of understanding these concepts in relation to solving the problem is emphasized.

Hello.
I am in confusion because I cannot understand which formula will be used in this and that derivation,because there are many formulas of physics.Then how we come to know that this specific formula must be used in this derivation
It is a great confusion for me.
Please solve my problem and define me the basic rules of physics derivations with some simple examples.
thank you.

When in doubt, start from the most basic. If you're in classical mechanics, it probably comes from Newton's laws. If you're in emag, Maxwell's equations.

Why don't you give an example or two of the kind of situation you're talking about? That would make it easier for people to share what their thinking would be in approaching a new problem.

Hello.
I am in confusion because I cannot understand which formula will be used in this and that derivation,because there are many formulas of physics.Then how we come to know that this specific formula must be used in this derivation
It is a great confusion for me.
Please solve my problem and define me the basic rules of physics derivations with some simple examples.

If there were a set of simple rules for derivations, physics would be a heck of a lot easier. :tongue2:

Try using a little ingenuity. This is what separates us from machines...

Example of my Queston.

Tide said:

Why don't you give an example or two of the kind of situation you're talking about? That would make it easier for people to share what their thinking would be in approaching a new problem.

It is an example of my question.
I is taken from the Chapter-Electromagnetism.
The topic is. “Force on a moving charge in a magnetic field”

Calculation of force on a moving charge in a magnetic field.
Force on a current carrying wire of length L in a magnetic field FL = I(L*B) -------- (1)
Here I have a confusion that is .
How we came to know that to find the formula, first we have to find out the total charge carriers in AL (volume) ?
Let.
Number of charge carriers in unit volume = n
Volume of a wire segment = AL
Number of charge carriers in AL Volume = nAL

Similar Reason?
Let
Charge on one charge carrier = q
Total charge Q = nALq

Now
Time = Distance/Velocity
t = L / v Here: why we find out time.?

We know that
I = Q / t Why we use I = Q / t to find current ?
I = nALq / L /v

I = nAqv put in equation (1)
Total force F =nAqvL*B --------- (2)
As L & v are in same direction
Why we took this step of unit vectors.?
So
L^ = v^
Hence
vL = vLL^
vL = vLv^
vL = Lvv^
vL = Lv

Equation 2 Becomes
Total Force FL = nAqLv*B
Let force on one charge carrier = F
Force on nAL charge carriers = nAL*F
Total force F = nAL * F
F = F / nAL
Put the value of F
F =nAqLv * B / nAL
We get
F = q v * B

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dear friends I think I could not explain it properly but I hope you will be understand this.I request you to solve my this problem that is : when and where we use the related formulas in any mathematical prove of physics.
Only this is my problem that I could not understand till now.
thanks.

As was mentioned before, there is not necessarily one simple set of rules to follow in order to tackle a physical problem. What works the best in learning how to solve physics problems is actually doing them, that is, practice. It's something you have to do in order to really learn.

The problem is to calculate the force acting on a current carrying wire in the presence of a magnetic field. You need to know a few things before you can solve the problem.

First, you have to know that a magnetic field produces a force on a moving charge. This is the Lorentz force and you would have to know that the magnitude of the force is the product of the charge, the speed of the charge and the strength of the magnetic field. The direction of the force is perpendicular to both the magnetic field and the direction in which the electron is moving.

That applies to a single charged particle so the next question is what is the net force on a collection of moving charges since that is what we mean by electrical current. The answer is that the net force acting on the wire (or current) is the sum of the forces acting on the individual charges. (In this case, only the electrons are moving.)

So we need to find a way of relating electrical current (which we can measure) to the number of electrons and their speed. The electrical current is the charge carried by number of electrons that pass by a given point in a period of time. Let's see where that leads us.

Suppose the electrons are moving with speed v and that there are n electrons per unit volume. How many of those electrons pass by a given point in some period of time? Imagine you could put a mark on the wire as a reference point and that you can take two photographs of the electrons, one at t = 0 and a second a short time later, call it t = T. Your photograph will show that the electrons that started out at your reference point will have moved some distance along the wire and, since we know the speed and the time the distance they traveled was just vt! Meanwhile, other electrons had moved in behind those advance electron to fill the space behind it.

How many electrons crossed your reference point? That would be all the electrons that now (in your second photograph) fill the space between those leading electrons and your reference point. Since we know there are n electons per unit volume and if the wire is uniform then the number of electrons that passed your reference point will be

$$n \times A \times v \times T$$

which represents the number of electrons per unit volume times the volume occupied by all the electrons that passed by your reference point during the interval of time T and A is the the cross sectional area of the wire. Now, just divide by T and multiply by q and you have the electrical current!

$$I = n \times q \times A \times v$$

Now, let's return to the first part. The magnetic force on a single charge is qvb (assuming the electrons move perpendicular to the field). The total number of electrons in the length of wire is nAL so the total force on all the electrons is nAL times qvB or

$$F = nAL \times qvB$$

But, naAv is just the electrical current so

$$F = ILB$$

You can generalize the argument if the wire is not perpendicular to the magnetic field.

Is this what you were asking for?

A general trick I've found for proofs is checking units. It may sound obvious or simple, but if you know what units you're trying to find, it's a lot easier to know which formulas to use.

It looks like you're using "a derivation of the important formula"
as if it were "an example pattern to solve problems by".

(In my view, qv x B is "better than" I l x B )
Draw a current cylinder of length l that the charge q travels in 1 sec.
Look at the diagram and see that qv = Il ... units: [Cm/s = C/s *m].
Now that you know this, remember one, and replace if need be.

What I mean is that regular humans *remember* that qv x B
... because that is the effect of B
... You don't have to work so HARD if you work SMART.
Pay attention to the CONCEPTS - organize by cause & effect!
...that means 2 important equations for each quantity.
You wrote I = Q/t because that's what causes current.

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## 1. What are the fundamental rules for physics mathematical derivations?

The fundamental rules for physics mathematical derivations include the use of basic mathematical operations such as addition, subtraction, multiplication, and division, as well as more advanced concepts such as calculus, differential equations, and vector algebra.

## 2. Why are mathematical derivations important in physics?

Mathematical derivations are crucial in physics as they provide a way to mathematically describe and explain physical phenomena. These derivations allow us to make predictions and calculations based on the laws of physics, ultimately helping us understand the natural world.

## 3. How do you approach a mathematical derivation in physics?

When approaching a mathematical derivation in physics, it is important to start with a clear understanding of the problem and the relevant equations and principles. From there, you can use logical reasoning and mathematical techniques to manipulate the equations and arrive at a solution.

## 4. What are some common mistakes to avoid in physics mathematical derivations?

Some common mistakes to avoid in physics mathematical derivations include not clearly defining the variables and assumptions, skipping steps in the derivation, and using incorrect mathematical operations. It is also important to double-check your calculations and make sure they are consistent with the laws of physics.

## 5. Are there any tips for improving skills in physics mathematical derivations?

Practice is key to improving skills in physics mathematical derivations. It is also helpful to break down complex problems into smaller, manageable steps, and to seek out resources such as textbooks, online tutorials, and practice problems. It is also important to develop a strong understanding of the underlying principles and equations used in the derivations.