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0answers
10 views

Problem in understanding the assumption made to find the vector-field in an arbitrary-shaped metal

Let there be any block of metal & inside it there is a point source of heat energy. Apart from that point, at all other points heat is in local conservation. Now, in order to find out the heat ...
0
votes
1answer
22 views

Flux from cube: Relation between the vector field to that of the opposite side

This is an exerpt from Feynman's lecture: . . .We wish to find the flux of a vector field $C$ through the surface of the cube. . . First consider the face having edges $\Delta y \quad \& ...
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votes
1answer
82 views

Why is $\int_{s} \mathbf{h}\cdot \mathbf{n} da = - \dfrac{dQ}{dt}$ & not $\int_{s} \mathbf{h} \cdot\mathbf{n} da = - \dfrac{dQ}{dt} .{dt}$?

I was reading the Lectures of Feynman about surface integral where a situation in which heat is conserved has been dealt. Let there be $Q$ heat energy present inside a body. Now, if there is net heat ...
0
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1answer
35 views

magnetic field due to current in a wire using Biot-Savart's law

I am learning about Biot-Savart's law to calculate the magnetic field due to the electric current in a wire. ...
3
votes
4answers
265 views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
0
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0answers
17 views

Does the heat flow vector depend on the proximity of isotherms?

Suppose, there be two isotherms at varying temperatures. Heat energy will flow from higher temperature isotherm to the lower; thus we can assign vector to each point & it will tell about the rate ...
2
votes
1answer
101 views

Insight into Torricelli's Equation ($v^2=u^2+2as$) [closed]

Torricelli's Equation ($v^2=u^2+2as$) is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) ...
0
votes
1answer
59 views

Using differentials to optimize a function [closed]

I've read in a paper by Tevian Dray an alternative way to solve optimization problems manipulating "differentials". Here is an example of how it works (next I quote the paper). Consider the ...
1
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0answers
19 views

Write the force as a sum [closed]

We suppose that a force $\overrightarrow{F}$ (for example, the gravity) is applied vertically downwards to an object that is placed at a plane which has an angle of $45^{\circ}$ with the horizantal ...
0
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0answers
33 views

Bulk Modulus and its derivative for a fcc lattice

The bulk modulus $B = - V \left(\frac{\partial P}{\partial V}\right)$. At constant temperature the pressure is given by $P= -\frac{\partial U}{\partial V}$, where$ U$ is the total energy. We can ...
1
vote
3answers
174 views

Problem in deducing the equations of motion using indefinite integral

As we know, antiderivative or indefinite integral is the function the derivative of which gives the actual function. Let $F(x)$ be the derivative of $f(x)$ ie. the instantaneous rate of change of ...
3
votes
1answer
46 views

$v^2 = 2ax$ or $v^2 = ax$?

As far as I am aware, $v^2 = 2ax$ is the formula to find the velocity in various questions. If kinetic energy = work, $$\frac{1}{2}mv^2=Fx$$ $$mv^2=2max$$ $$v^2=2ax$$ We use this formula to solve ...
1
vote
0answers
72 views

What is the relativistic mass of this spinning ball? [closed]

Relativistic Mass is: $$ m_r = \frac{m}{\sqrt{1 - v^2/c^2}} $$ So Einstein says that the faster an object moves, the more mass it gains (relativistic mass). So suppose you have a spherical ball ...
0
votes
0answers
23 views

Solve unsteady-state pressure-falloff axial gas flow equation for permeability

Equation 17 in Section 6.2.1.2 of American Petroleum Institute Recommended Practices 40 for Core Analysis gives a permeability equation of: $$ ...
0
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0answers
25 views

Average value of function [duplicate]

Can anyone help me in solving Q .1 & .2? Also I am confused at one point. In $F(x+p)$ where $p$ is period. It means that the function is at the point period plus $x$ dist. Away.So how can I put ...
0
votes
0answers
14 views

Find center of mass and moment applied on beam structure. [duplicate]

I have a simple mathematical problem to solve but it is giving me a slightly difficult time to figure out. The problem: I have a beam structure with same cross section. It consists of three beam. ...
4
votes
2answers
568 views

A basic math identity often used in integrals [closed]

I'm just wondering about why $y_i=A_{ij}x_j$ implies $$d^Ny=|\det A|d^Nx.$$ I see that $\det A$ is the product of the eigenvalues of a diagonal matrix but still don't exactly see how. Please help.
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3answers
118 views

What is physical interpretation gives integration?

It is my understanding that the integration is the inverse process of differentiation and its meaning is a fine sum (in fact, so is its symbol) but what physical interpretation do we get from this? At ...
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6answers
643 views

Is Newton's first law something real or a mathematical formalism?

Why do objects always 'tend' to move in straight lines? How come, everytime I see a curved path that an object takes, I can always say that the object tends to move in a straight line over 'small' ...
0
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0answers
39 views

Understanding the advantage of using integration over summation for finding COM for a continuous body?

My book (NCERT) writes: In a rigid body, such as a metre stick, the number of particles is so large that it is impossible to carry out the summations over individual particles. Since the spacing ...
1
vote
1answer
59 views

Can moment of inertia be defined as function of mass?

For continuous bodies, moment of inertia is found as $$ \int dI = \int_{m_i}^{m_f} r^2(m) .dm$$ . Now, $$\int dx = \int_{u_i}^{u_f} f(u).du \implies X_f(u) = \int_{u_i} ^{u_f} f(u) .du + X_i(u)$$ , ...
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votes
2answers
109 views

Is the Fundamental Theorem of Calculus really applicable to the definition of work?

When the force $F$ on an object is not constant, then the work it performs is defined as $$W = \int_{x_0}^{x} F(X)dX.$$ Now, the Fundamental Theorem of Calculus states that $$\text{If}\,\,\, f(x) ...
1
vote
3answers
70 views

Problem in understanding the process of calculating the rotational inertia

As we know, rotational inertia is the mass-equivalent in rotation. For a discrete body, it is measured as $$I = \sum m_i{r_i}^2 $$ . But when a continuous body comes, $$I = \int r^2 .dm$$ which ...
1
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5answers
323 views

What is divergence?

What is divergence? I was learning about Maxwells equations and don't understand the divergence part of it. Can someone give an intuition of what divergence is in relation to maxwells equation. To ...
3
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2answers
435 views

Why and when do we differentiate or integrate equations in physics? [closed]

I'm an engineering student and none of my professors ever explained why do we use derivations and/or integrations in physics. So I have this task, it goes like: The object is moving in a positive ...
1
vote
1answer
103 views

Integration by parts [closed]

Zee in his book, Quantum field in a nutshell mentioned the following, p. 22: Equation (14): $$Z=\int{D\phi}e^{i\int d^4x{ {\frac{1}{2}[(\partial \phi)^2-m^2\phi^2]+J\phi}} }$$ He said then, ...
4
votes
4answers
2k views

Wrong calculation of work done on a spring, how is it wrong?

So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring ...
11
votes
4answers
399 views

Electromagnetic field and continuous and differentiable vector fields

We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields. We know electrostatic and ...
6
votes
2answers
2k views

Application of Calculus in Physics

Why do we apply Calculus in Physics when most of the quantities are not continuous and are not symmetrical at all levels of magnification? Aren't most, if not all, forms of Matter and Energy discrete? ...
3
votes
2answers
125 views

Why are some variables summed infinitesimally and others aren't?

This is something that has been bothering me and I hope the title kind of makes sense. It may be a stupid question but please be gentle. My question is, let's say we have current: $$I=\frac{dq}{dt}$$ ...
0
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0answers
22 views

Integration in the three coordinate systems [duplicate]

I need a book teaching triple and double integrations in the three coordinate systems and teaching vectors in three coordinate systems with no in depth mathematics. I need it to help me in general ...
4
votes
1answer
107 views

How is taking the average of an integral over an interval justified?

I have been studying classical mechanics. Often when going through a worked problem, I see a step where there is an integral from 0 to 2$\pi$ of $\sin^{2} \theta \ d\theta$. Instead of using the ...
0
votes
0answers
29 views

Calculate static magnetic field in a volume of air with known sample points

So I know some calculus and I know some linear algebra, but do not really master electromagnetism (did a course ten years ago). There is a problem someone else has solved in a matlab script for me ...
2
votes
1answer
76 views

First variation of the action in relativistic notation - Landau & Lifshitz “Classical theory of fields”

In Landau & Lifshitz's book, Classical theory of fields, the action for a free particle is defined as: $$\tag{8.1} S= \int ^b _a {-mc \ \text d s}=0,$$ where $$\text d s=c\,\text d ...
0
votes
2answers
80 views

Electric Field and Calculus: What is the physical significance of infinitesimal $dA$ in the equation of Gauss's Theorem?

In many equations we see infinitesimals $dA$, $dS$, $dx$ and so on. What is is the physical significance of these? Someone told me it signifies a small entity. For example,in case of $dA$ it signifies ...
1
vote
1answer
112 views

Difficulty with the usage of Cauchy's integral formula in Griffiths QM book

On page 410 of Griffiths QM 2nd Ed. book, he begins an analysis to evaluate the integral: $$\frac{1}{2i}\int_{-\infty}^\infty \frac{s \sin{(sr)}}{(s-k)(s+k)}\mathrm{d}s.$$ To exploit Cauchy's formula, ...
1
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3answers
107 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
1
vote
0answers
38 views

What is the relationship of the curl of a vector with its conservativeness? [closed]

My Physics teacher told me that a conservative field has zero curl.But I am not getting the logic behind it...I am even not clear why the curl represents how much the vector field swirls around the ...
2
votes
1answer
127 views

Landau's derivation of a free particle's kinetic energy- expansion of a function?

I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact ...
-1
votes
1answer
85 views

Work to pump water through a hole in a trapezoidal prism

So I don't want to give the full details of the problem I'm working on, since I want to solve it myself. But I'm not sure which physical principles I'm supposed to use, since this is a Calc 2 ...
0
votes
0answers
60 views

Finding the total space that an oscillating body has gone through via complex analysis

I was solving my homework and I got to an exercise that stated: An harmonic oscillating body has an equation of $$y(t) = A \sin(t)$$ Find the total space that the body has travelled during $t \in ...
1
vote
1answer
477 views

Inverse Fourier transform of Yukawa potential (troubles with Mathematica)

It can be proved that the potential $\frac{e^{-u|r|}}{|r|}$ has Fourier transform $\frac{4\pi}{u^2+q^2}$. Now, I'm trying to go backwards and do the inverse Fourier transform but I'm running into ...
0
votes
2answers
94 views

$R = dV/dI$ for varying temperature

I'm trying to do my prelab for an E&M course, and am asked if, for plotting $V$ vs $I$ with a varying temperature, I should expect a linear slope. I know that both $V$ and $I$ depend on $R$, and ...
3
votes
4answers
152 views

Based on note, how fast is a stringed instrument's string oscillating?

to be quite honest, I have no idea where to start on this problem mathematically. However, it struck my curiosity and would love to know how it works on a mathematical level. the problem You have a ...
0
votes
0answers
99 views

Integration of Forchheimer equation for unsteady-state permeability determination

I would like to know the steps for the integration of Equation 17 in Section 6.2.1.2 of American Petroleum Institute Recommended Practices 40 for Core Analysis to yield: ...
0
votes
1answer
53 views

Inconsistent integral and distance in spherical coordinates

I am currently studying this problem: 14 b) There you see an integral $$A(r) = \int f(\theta) (-\sin(\phi), \cos(\phi),0) d \Omega$$ where $f$ is the function containing all the rest of the integrand ...
2
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0answers
28 views

Book for multivariable calculus [duplicate]

Hi I want to start learning multi variable calculus specifically for learning electrodynamics. What are some good text books?
4
votes
1answer
213 views

Newton's original proof of gravitation for non-point-mass objects

Suppose we have two bodies, one very large (Earth), and one very small (a cannon ball). If the cannon ball is some distance away from the Earth, to find out the force produced on the cannot ball, we ...
3
votes
0answers
230 views

Heat transfer from hot water through a copper pipe to oil in a tank

I want to build a geyser attached to a pump with copper tubing running into an oil tank. This is done because the oil solidifies at a temperature below 15 degrees Celsius. I have done a few ...
1
vote
0answers
65 views

Applications of Calculus 2 to Physics [closed]

Im teaching a section of Calculus 2 (integration techniques, arc length, surface area, improper integrals, parametric & polar functions, sequences, and series ) next semester and would like to ...