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### Level-4 :: Problem and Solution Sets

Summary (or abstract) not available for this node.
kapoor 20/04/19

kapoor 18/04/19

### Problem-EM-05004

A point charge $$q$$ is embedded at the center of a sphere with dielectric constant $$\kappa_1$$. The sphere is itself embedded in an infinite volume with dielectric constant $$\kappa_2$$. Find the electric field out side the sphere and surface charge density on  the surface of the sphere.

kapoor 18/04/19

### Features of Proofs Programme

The project team :  Ranjan Shrivastava and A. K. Kapoor.

Based on a work at http://0space.org/users/kapoor.

 This work is being pursued with a philosophy of working without attachment expressed beautifully by Sri RamKrishna Paramhansa who once said, “To work without attachment is to work without the expectation of reward or fear of any punishment in this world or the next. Work so done is a means to the end, and God is the end.”

 Why repeat a lots of things ? Why repeat all this? Because there are new generations born every day.  Because there are great ideas developed in the history of man, and these these ideas do not last unless they are passed purposely and clearly from generation to generation.                      ===            Richard Feynman (1998)

Many of the content are not my original, they  are 'Other Men's Flowers'. My views on this issue resonate with the ideas in the article titled "Montaigne on “Curation,” the Illusion of Originality, and How We Form Our Opinions"

kapoor 15/04/19

kapoor 14/04/19

### Problem/EM-10005

An inductor, made up of a very long air-core solenoid of length $\ell$, radius $r$ and  $n$  turns  per  unit  length, carries a current $I$.  For  $\frac{dI}{dt}>0$,  verify  that $$\frac{dU_B}{dt} = -\iint_S \vec{S}.\overrightarrow{dA},$$  where the surface $S$ in the surface integral in the right hand side is the surface that encloses the solenoid and $$U_B$$ is the energy density associated with the magentic field.

Analysis

You need to understand the following. Read the given question several times and answer the following questions. After making sure that you have correct answers and that you understand them as well, try to solve the problem.

1. What is Poynting theorem?
2. What does $\vec{S}$ in \EqRef{EQ02} stand for?
3. What is the expression of the Poynting vector?
4. What physical quantities do the symbols $U_B$ and $\vec{S}$, in \EqRef{EQ02}, represent?
5. Is it correct that the expressions for the quantities $\vec{S}$ and $U_B$ involve $\vec{E}$ and $\vec{B}$? If not, what is the correct expression?
6. What field(s) does the solenoid produce? Magnetic field $\vec{B}$? Electric field $\vec{E}$? Both of these? None of these? Do you know the expressions?
7. Compute the magnetic field produced by the solenoid. Write zero as your answer if it does not produce it.
8. Repeat the above question for the electric field.
9. Find $\vec{S}$ in terms of current $I$ and compute the surface integral $\iint_S \vec{S}.\overrightarrow{dA}$. Find $\vec{S}$ on the sutface of the solenoid.
10. What will be the volume integral of $U_B$?
kapoor 13/04/19

### Problem/EM-10004

Summary (or abstract) not available for this node.
kapoor 13/04/19

### EM-Mod10-Conservation Laws

Summary (or abstract) not available for this node.
kapoor 13/04/19

### EM-Mod11:: Electromagnetic Waves

Summary (or abstract) not available for this node.
kapoor 13/04/19

### Quantum Mechanics :: Level 3

Summary (or abstract) not available for this node.
kapoor 13/04/19