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1answer
39 views

Current Electricity

If $$ \frac{dQ}{dt} = I $$ and if an accelerated current produces E.M. waves (radiation), does that mean $d^2Q/dt^2$ (second derivative of a charge w.r.t. time) will give me the magnitude of the wave ...
-1
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0answers
23 views

2-Dimensional motion query [closed]

Question: A body is projected with speed u at an angle theta with the horizontal. (Following are the three parts in the question). Find the change in velocity in time t. Find the speed of body at a ...
1
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2answers
125 views

Composing integrals in physics?

OK... so this problem isn't really specific... it's more of a conceptual puzzle. I've recently started using integrals while solving problems in physics (specifically Newtonian Mechanics and other ...
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0answers
49 views

Compute distance travelled based on a yaw-rate

Assume that a rigid body is traveling with constant velocity $v$, and (this rigid body) is rotating with a constant yaw rate of $\dot{\theta}$. Find the distance travelled in one time step, $\Delta ...
1
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0answers
32 views

quantum determinant calculation [closed]

Heyho, i've got problems understanding a certain calculation of the trace of an operator valued matrix right now. We've got the Matrix $T(\lambda)= \begin{pmatrix} A(\lambda) && B(\lambda) ...
0
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2answers
81 views

Physical meaning of divergence

While reading the section on Hamiltonian mechanics in Taylor's Classical mechanics, I realized that I didn't fully understand what he was saying when he was explaining why ...
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3answers
158 views

How do we calculate instantaneous velocity in 2D?

Suppose a body is moving with a constant speed of $10~\mathrm{ms^{-1}}$ in negative $x$ direction in $x$-$y$ plane. Let $\vec r$ be the position vector. Then what will be the instantaneous velocity ...
2
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2answers
83 views

Falling rain drop problem

I've been trying to solve this physics problem today "Spherical raindrop falls through a cloud with uniform density. After falling 1km it has a radius of 5mm. What volume fraction of the cloud is made ...
1
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1answer
59 views

Why is the elemental volume of a sphere equal to $4 \pi r^2dr$?

I was doing this question on calculating the electric field at a certain point in a sphere (length $r$ away from the centre), where the charge density is given by an equation. When I checked the ...
2
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3answers
342 views

Basic question about acceleration [duplicate]

Very basic question. Please show where I'm wrong in the following reasoning. The movement of an object in function of time could be described as $$ x(t) = v t + x_{i} $$ if velocity is constant. If ...
4
votes
1answer
68 views

Optimization of Bottle Rocket Water Level

My (entry-level) physics class is building bottle rockets, and we are competing to build the longest-flying bottle rocket. The rockets are filled partway (we get to decide how much to fill them) with ...
1
vote
2answers
142 views

Derivation of Jefimenko's Equation in Jackson's EMT book

I have been trying to understand the derivation of Jefimenko's equation in Jackson on p.246-247 which can be seen in the photographs attached. First of all I did not fully comprehend the ...
2
votes
2answers
92 views

Differential operators in curvilinear coordinates

In the appendix A of Griffith's Electrodynamics text, he cites Spivak's Calculus on Manifolds as a reference more a more complete treatment of taking the gradient, curl, divergence, and Laplacian in ...
0
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1answer
45 views

Simplifying a Vector Integral

This question has (long) remained unanswered on MSE. While reading the book - Theory and Applications of Boltzmann Transport Equation by Cercignani, I found this integral which I am unable to ...
3
votes
1answer
72 views

What is the physical cause that circulation on a closed surface is zero?

This is quoted from Feynman's Lectures: We would like to see what happens when the loop shrinks down to a point, so that surface boundary disappears - the surface becomes closed. Now, if the ...
0
votes
1answer
48 views

Confusion regarding area from graph

This might be a trivial question but is illustrated below. Why is the area 'below' the graph always taken for a velocity-time graph when finding the displacement? I mean why is the area with the time ...
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0answers
12 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
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1answer
24 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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1answer
85 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. ...
0
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1answer
86 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 ...
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0answers
26 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
197 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
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1answer
66 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 ...
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0answers
78 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 ...
3
votes
1answer
61 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 ...
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0answers
103 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 ...
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0answers
33 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: $$ ...
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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
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0answers
15 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. ...
-1
votes
3answers
129 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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0answers
52 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
76 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, $$\int dx = \int_{u_i}^{u_f} f(u).du \implies X_f(u) = \int_{u_i} ^{u_f} f(u) .du + X_i(u)$$ , ...
0
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2answers
116 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
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3answers
76 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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3answers
255 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
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2answers
1k 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
123 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, ...
1
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5answers
481 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 ...
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
114 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 ...
4
votes
2answers
579 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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0answers
33 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
93 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 ...
3
votes
2answers
129 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
votes
2answers
129 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 ...
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4answers
442 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 ...
1
vote
1answer
129 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, ...
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3answers
109 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
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0answers
40 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
169 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 ...