Taken together, the two different paths between A and B form a closed loop. To see this, go along P1 from A to B, then go along P2 from B to A. If the integral along this loop is zero, then that means that the integral of P1 from A to B is equal and opposite to the integral of P2 from B to A...
The electric field lines are a representation of the direction of force that a test charged particle would experience. In your example, the 2nd positive charge would still be repelled from the 1st positive charge and attracted to the negative charge.
One of the biggest things that gets me is the concept of relativistic mass, i.e. that mass increases at relativistic speeds. It's led to more than a few misunderstandings on these forums, mostly from thinking that a fast enough particle will turn into a black hole because of it.
You are making the assumption that you are grounded. Pretty much the only way you can have the charge flow through your body to the Earth is if your body was in contact with a grounded conductor.
They are two different properties that have the same effect. Your first source, which discusses the covalent bond, is generally talking about molecules, while the other source is talking about individual atoms. If a molecule has a strong covalent bond, it generally makes a good insulator because...
I believe the beginning they are talking about a chemical battery; it talks about moving the charge from a low energy state to a high energy state.
In a battery, a chemical reaction supplies the energy to separate the charges between the cathode and anode, which causes an electrical potential...
You have already been given answers by the others in this thread. They have told you that moving neutral matter does not generate magnetic fields, and gave you a reference to where you can learn more about magnetism. You then go on to argue with the people you are asking help from. That is not...
It's not that you can't use the divergence theorem, as it holds no matter the case. You cannot use cylindrical symmetry to simplify the system because the E field in the system will not be cylindrically symmetric. To prove this to yourself, take the shape of the field when z>>L.
Even as a...
There would still be an induced momentum. As the magnetic field comes through, it would be a time varying field at the surface. Since -dB/dt = curl(E), there would be an equivalent electric field at the surface pushing the charged shell the other way.
This won't change the fact that the momentum of the sphere changes; it would only mean that the momentum of the sphere is indeterminate.
But the magnetic field generated by the moving charge inside is not spherically symmetric, it curls around the axis of motion of the moving charge. The...
You aren't measuring the velocity, you are measuring the radius of curvature of the beam.
When you find the curvature, you plug that in, along with other values into an equation to find the e/m. For a given velocity and magnetic field strength, the e/m is given by e/m = v / (r B). So as the...
Let me elaborate a little on what jtbell said.
As the particle passes through the capacitor (let's assume that it enters at the exact midpoint between the plates), it will be deflected to the side. As it moves closer to one plate, the electric potential will drop because it will be farther from...
I think you may be over-thinking it. If df(t)/dt = C, then f(t) can be written as f(t) = f(0) + Ct, i.e. a first order Taylor expansion.
That means that f(t) = <A>t can also be written as <A>t = <A>0 + d/dt(<A>t) * t.
Think about it. The lab makes the simplifying assumption that the velocity is uniform throughout the trip of the circular path; as noted, the electron slows down because of interaction with the rarefied gas in the chamber. This means that the true average velocity is lower than the assumed...
I have never seen a field where the all of the grass sticks out of the ground completely vertically. Even if they aren't laying flat, they are always bent over in one direction or another. For example...
Imagine you are in a big grassy field. All over the ground and everywhere you look there are blades of grass of every variety. Even though they are different, they all have a length and a direction.
Say you wanted to compare and record the blades of grass; one of the things which you would do...
The pVγ=const describes the relation between the pressure and the volume of a gas while it undergoes an adiabatic process. The exponent γ is the ratio between the specific heats at constant pressure and volume, Cp / Cv. That means that the dimensions of the constant can be different for...
The ball will not move any faster than the drive wheel of the launcher; so once the ball reaches the same angular speed of the drive wheel it will not experience any more angular acceleration and the torque on it would reduce to zero. Remember, torque is the rate of change of angular speed.
A...
When dealing with indeterminate forms like 0/0, one method is to take the limit as the numerator and denominator go to zero. It's exactly the same as L'Hospital's Rule, since the derivative is the limit of the difference quotient.
All that it really means is that the contribution of that...
The easiest way, I think, is to look at the integral as the limit of a Riemann sum of charge in the volume element ΔV as ΔV → 0 , which would give the indeterminate form ΔV/Δr2 → 0/0. Since the volume element in the numerator goes as x3 and the denominator goes as x2, that means the numerator...
It is often convenient to make calculations based on intensity instead of temperature. In fact, most non-contact devices which measure temperature first measure intensity and then do a calculation.
And a fundamental unit is one which can only be measured, not derived from another. As rbj said...
Usually, we like to see what efforts have been put into a solution. It helps us know where you are stuck; it also makes sure we aren't doing all the work for you, which would make the learning process more difficult.
So please, show what you've done towards a solution so far.
As said before, it is because of the chain rule.
When you have a function which depends on y, f = f(y), where y depends on x, y = y(x), the derivative df/dx can be multiplied by dy/dy (which is 1 and so does not change the value) and reorganized:
\frac{df}{dx} = \frac{df}{dx}\frac{dy}{dy}...
Since number of photons per time interval is only dependent on the intensity, then only intensity affects the current.
Higher frequencies may increase the energy of the ejected photoelectrons and make it cross a distance faster, but the time between each successive photoelectron remains the...
I think what Simon Bridge is saying is that the speed of propagation through a medium is dependent on frequency, with emphasis on "through a medium".
The ratio of the speed of light in a vacuum to the speed of propagation through a medium is the index of refraction for that medium. The fact...
In your first example, if you only look at the object-earth system, then yes, it gains mgh energy in the form of potential energy, and the total energy is not conserved. However, if you include the person lifting the object in the system, then the object still gains mgh energy, but the person...
Since atoms are made of equal numbers of protons and electrons (and neutrons, but they don't make charge), when the electrons are transferred it leaves an atom with more of one or the other. Protons themselves are particles that have a positive charge, while electrons are particles that have the...
Specifically, Earnshaw's Theorem states that in a static situation for pointlike particles, a 1/r potential does not have any maxima or minina (stable points) in an unoccupied region, since the sources themselves occupy space. When dynamics are added into the mix, there is an effective potential...
F = ma
The accelration only depends on the total force applied and on the mass that is being accelerated. Since there is no force on the ball when not in contact, it will not be accelerated, so the only thing being accelerated is the ship. Since the only thing being accelerated is the ship and...
Ok, let's use some actual formula's for this. Suppose a rocket with an object inside had been constantly accelerated and then instantly reversed the direction of acceleration. At the moment that the acceleration changed, it had a velocity v_0, and we label the location as the origin. The...
I believe that the sealing strip on most refrigerators are magnetic to help hold the seal and keep the door closed. That magnet would require a bit extra pull to get the door open.
But also, the effect of the door needing to push the air in front of it out of the way isn't negligible...
How do you manage to get this? Ignoring elastic rebound, they would appear to accelerate in the opposite direction as the rocket, with the same magnitude.
And how would you tell the difference between constant accelerating and gravity in a soundless, windowless car?
Unless the direction...
http://en.wikipedia.org/wiki/Hubble's_law"]http://en.wikipedia.org/wiki/Hubble's_law[/PLAIN] [Broken]
"Although widely attributed to Edwin Hubble, the law was first derived from the General Relativity equations by Georges Lemaître in a 1927 article where he proposed that the Universe is...
His definition of the distance of partial obstruction spans when the front bumper is the same distance from the stop sign as the other car's rear bumper, to when his rear bumper is the same distance as the other car's front bumper.
Assuming the other car is stationary at the stop sign, this is...
Well, when you doubled the voltage, you quadrupled the power that the resistor had to dissipate, since P = V2/R. At 5V, the resistor was dissipating 25/51 = 0.49W. But at 10V, it went to 100/51 = 1.96W.
And looking around I found this: http://www.instructables.com/file/FCSUQFCGJQEDD5L/. It...
It depends on the way in which it moves. The dipole would only experience a torque on it if it were rotating with respect to the B field. If the dipole was moving without rotation, it would not experience a torque but would experience a force on its center of mass. If it was only rotating, it...
The slope of a line tangent to a function at a point is the same as the value of the derivative of the function at that point, by definition; this also means that the derivative of the tangent line at a point is the same as the derivative of the function at that point, so y'_{line} = y'_{curve}...
The pressure in a fluid at depth z from the surface is P(z) = \rho g z, where \rho is the density of the fluid, and g is the acceleration due to gravity.
The get the total force on a surface, the pressure would need to be integrated across the surface.
F = \int \limits_S P da
For a...
If you are given ds^2 = dx^2 + dy^2, then s \neq \sqrt{{x'}^2 + {y'}^2} .
Take ds^2 = dx^2 + dy^2, divide it by dx^2 and then simplify. (hint: \frac{dx}{dx} = x' = 1)
I sounds like you are mixing up electric polarization with magnetization.
What would happen is that when the bar is near the surface of the Van de Graaff generator, the positive charge of the generator would create an electrostatic field which would attract the electrons in the metal causing...
There is also the issue of mechanical safety, since cyclotrons generally require a high vacuum to function. The equipment used to create vacuums are dangerous, as well as pulling a vacuum with inadequate materials could lead to violent implosion.
Most of the time, it is enough to give the final equation in implicit form. To find the constant, you plug in the initial conditions: ie, y(2) = 2 means that x=2 and y=2. If the initial conditions were y(5) = 3, then it would be y=3 and x=5.
A minor nitpick but there's an algebra mistake in...
I suggest you take that up with my Thermodynamics textbook, and wikipedia for that matter. They both state that PV is a state function. The textbook was Carter's “Classical and Statistical Thermodynamics” 2nd edition.
And as far as p versus P, the textbook I used had used P for pressure...