Recent content by Chandra Prayaga

Is this question still running? I believe things would be clearer if standard symbols with superscripts and subscripts are used. As far as I can see, the problem is the following: The Hamiltonian is: H = ω0Sz The state of the system is, for example: (1/√10) |+> + (3/√10) |->, where the states...

All uncertainties of negative signs are removed by drawing a picture. Draw the diagram with the x axis, show the proton moving to the right (in the + x direction). Now ask the question, what direction should the force be to stop the proton? That will also give the direction of the electric...

A diagram would help in understanding what the symbols and the formulae mean. I am not sure where the second formula Ec(f) = Ec(i) - Ec(f), comes from.

As PeroK pointed out, your expression for <x> is wrong. Also note that there is a difference between differentiating <x> and differentiating either ϕ(x) or its square which is the probability density: The probability density is a function of x, whereas <x> is not. <x> is a definite integral...

I frankly don't understand the need for "Fleming's left hand rule". This is indeed the Hall effect, and everything is explained by the lorentz force law, which uses the standard right hand rule for all cross products of vectors. I think an extra rule for particular cases (such as the electron)...

What was your reason behind your choice?

Did you use the information that it is a Carnot cycle?

There was nothing wrong in what you worked out. As haruspex pointed out, identify yi and yf in your own algebra and you are done.

Check your derivative dV/dt again.

Incidentally, the letters p, V, n, R and T are called "symbols" which stand for "variables". Your identification of symbols with variables was correct.

In your ideal gas equation pV = nRT all the quantities are given, except n. So solve for n. That is the first step. Now to nswer (ii), you need to know how many atoms thyere are in one mole of the ideal gas. Do you know that?

There are a couple of steps in the logic before you can come to a conclusion. First you should make a drawing of the field lines or arrows inside the hollow, keeping in mind that the electric field is perpendicular to the surface of the conductor.

Remember that the electric field must be perpendicular to the metallic surface, in equilibrium. That will be so inside the hollow too.

Let us look at your question step-by-step. Place the metal spherical hollow conductor in a uniform electric field inside a capacitor. If the elctric field penetrated into the hollow region, what would be the shape of the electric field lines inside the hollow?

Also draw the arrows in the diagram showing the fields that you want to calculate.