The expression you wrote down for $$ \lambda = \nu T $$ should give you the quantum tunneling rate. To find the lifetime of the particle in the well, find the reciprocal of the rate.
As you noted, the gradient operator takes a scalar in R and gives a vector in $$R^n$$ and each derivative of f in the sum gives a component of the resulting vector. The key here is that the differential operators all act on f and they act differently. For instance you can have f = xy, taking the...
Work(significant work) is done at two stages i.e. at the higher temperature isotherm (isothermal expansion) and at the lower temperature (isothermal compression). In between these processes we have adiabatic expansion of the gas where the gas cools to the lower temperature. The key here is that...
You have to be careful here, the intensity is proportional to the square of the electric field i.e. $$I \alpha \epsilon E^2$$. Hence you expect the energy/Intensity to be a 1/4 of what you would get when E-field is 1/2 of its original value.
A net force would cause a body to linearly accelerate in the direction of the force. In this case there is zero net force so the gyroscope does not linearly accelerate. However, because the weight and normal force are not aligned, there is a net torque, this is what is responsible for the...
I am a bit confused by which rotations you refer to at what point but I'll assume you have a 'spinning' gyroscope (along the gyroscope's axis) whose axis is 'precessing' (about where the gyroscope is pivoted) under the influence of gravity. The motions can be found by carefully considering the...
I find the statistical physics interpretation more satisfying. Entropy can be considered as the amount of ignorance we have about a system. For example, we can know the system's macrostate (i.e. its temperature, internal energy etc.) but we do not know what microstate it is in. Microstate here...
The expansion is basically a Taylor expansion about δq and δ{itex}\dot q{\itex}t keeping the first order powers in in the differentials. For a deeper understanding, read on functional derivatives and or the calculus of variations.
A conceptual, albeit incomplete way to understand why the radius of a black hole can be considered as what you stated is by considering that if nothing can escape a black hole (not really!), then the escape velocity of any particle from a black hole must be the speed of light which is the...
This is because the iron becomes magnetized. You can imagine the piece of iron as being made up of many tiny little magnets (domains) in random directions such that in the absence of an external magnetic field, all those little magnets cancel each other out. When the iron is placed close to the...
Always make sure sure you have the correct number of equations for solving the system. In these problems, if you have n coefficients you would expect n-1 equations such that all the other coefficients can be expressed in terms of the incoming wave coefficient. These equations come from matching...
Ta represents the atmospheric temperature (cold reservoir) and Tc represents the higher reservoir temperature. The expression (1-Ta/Tc) is what is called the Carnot efficiency. It's value is between 0 and 1 and it represents the maximum fraction of the heat energy absorbed at the the higher...
Current density is a local property (For a point), whereas current is a global property (e.g. for an entire wire). Both are useful depending on the problem but I guess I'll talk a bit more about current density. Densities in general are useful because they allow you to look at the effect of...
Hi all. I am an undergraduate student studying physics at MIT. I'm hoping to answer as many questions as I can and getting my questions answered as well. I realized I enjoyed answering physics questions and am hoping to be of use to the members of this community.
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