Here's something from wikipedia: "This classical Kelvin–Stokes theorem relates the surface integral of the curl of a vector field F over a surface Σ in Euclidean three-space to the line integral of ...

Short answer:Finite size of dust particles and inverse square law. The side of the dust particle towards the screen is negatively charged and the other side is positively charged.Now due to the ...

Let's revisit what the term "spectral energy density" means.It means the amount of energy emitted in a infinitesimal $d \lambda$ or $d \nu$. Now due the the relationship $\lambda=\frac{c}{\nu}$,we ...

We know about the existence of dark matter only from its gravitational interaction. In fact dark matter was devised to explain abnormal rotation curves of galaxies which required extra matter to ...

Let's find the complete solution of the problem. A complete solution of the problem would be the solution to the linear ODE, $m \dot{\mathbf{v}} =q\mathbf{v} \times \mathbf{B}-k \mathbf{v}$ Assume ...

Let me put it this way,all forces that we know arise from interactions between two particles/systems. This is true either for fundamental forces such as gravitation, electromagnetism as well as ...

I am not sure about the $\frac{1}{\sqrt{A^2-x^2}}$ part in you approximation. In the asymptotic limit $n \rightarrow \infty$,the Hermite polynomials behave as follows: The cosine part relates to ...

The $dx$ is a signed quantity. You don't need to put the negative sign explicitly.The infinitesimal displacement is always $dx \hat{i}$ and then $dW=\vec{F} \cdot dx \hat{i}=Fdx$.Whether the integral(...

Static friction always opposes relative motion at the point of contact. There are two cases possible: 1)It orients itself in direction and magnitude in such a way that the relative acceleration of ...

Assume the contrary,suppose a point exists such that the local charge density is positive,say point A. Now from Gauss' law the total charge on the inner surface is negative.So there must exist a ...

The answer lies in the fact of how frictional forces work."Frictional forces always try to oppose relative motion between surfaces(and if possible they will completely eliminate the motion between the ...

1) The optical path length for light travelling in a medium is defined as the path length that will produce that same phase difference(or rather contains same number of wavelengths) as light ...

The energy released/absorbed in nuclear reactions depends on the binding energies of the nuclei.So yes,energy is released in nuclear fusion of hydrogen to helium while energy will be absorbed in the ...

The water does fall down! It moves forward due to it's tangential velocity and falls down precisely the amount it is necessary to move in a circle.The argument is similar to why doesn't the moon fall ...

We can express the velocity of the particle as: $\vec{v}= \vec{\omega} \times \vec{r}$ where $\vec{\omega}$ is perpendicular to the plane in which $\vec{r}$ rotates and $\vec{\omega}$ can change only ...

Your thought experiment stumbles upon an important idea in electrodynamics which is quite counter-intuitive.The EM field produced as radiation due to the charge in fact produces a reaction force on ...

I think the relationships result from an interplay between the dependence of energy on quantum numbers and the volume element in the space of quantum numbers. For an $m$ dimensional particle in a box,...

There are two approaches that can be used: 1)The Bottom up approach This is done using atomic layer deposition.See wiki for more information. The second and more useful approach would be, 2)The Top ...

The force acting on the conducting bar will be given by: $$F=-ilB$$ But it is given that the bar has a negligible mass.So there can't be any force acting on the bar otherwise it would ...

For all conductors we can define a constant called the Capacitance such that, $$Q=CV$$ where $Q$ is the total charge on the conductor and $V$ is its potential. So yes,increasing the charge on a ...

The fact you are stating is quite general in fact and even extends in a related form to 3 dimensions also. It is known as Chasles's rotation theorem: Any general displacement of a rigid body ...

In classical electromagnetism,we have a force which depends on the acceleration(strictly it depends on its derivative). Abraham-Lorentz force: It is the recoil force a charge experiences due to the ...

The magnitude of the work done by friction in linear motion is equal to the work done by the torque of friction only if the wheel is smooth rolling. In smooth rolling,we have $$v_{cm}=\omega R$$(...

Let's start with the definition of a "perfect" conductor: A body in which electrons are free to move under the action of an electric field. Corollary-1:Under electrostatic conditions the field ...

In fact,the the given ODE can be easily solved even without computer assistance. $$r\ddot{\phi}(t) = -\mu \sqrt{r^2\dot{\phi}(t)^4+g^2}$$ This can be converted to, r\dot{\phi}(t)\frac{d\dot{\phi(...

Consider the given circuit as follows: The first thing to realize that it is hopeless to work with currents as our independent variable.In the end there are going to be three independent currents ...

Maybe finding the Julian date will help you. Julian days are used for astronomical purposes. Every day midnight occurs exactly when the J.D. (Julian date) is *.5. So you can convert the J.D. to U.T. ...

However, since h is decreasing over time, u is not constant and it has a decreasing parabolic shape over t. Why do you think the $u(t)$ must have a decreasing parabolic shape over time. I am ...