In the first page of my work, I guess everything MAY be comprehensible except the last biconditional...
In the book, it is written as:
This is equivalent to the following statement:
DEFINITION OF STEP FUNCTION: A function ##f## defined on a rectangle ##Q## is said to be a step function if(f)...
I need to do this because I am having difficulties in quickly comprehending that book. The encrypted one is much more easier for me to make sense of what the book is saying. Also the book has skipped several trivial proofs.
The following 3 pages are extract from the book: "CALCULUS VOL II" by Tom M. Apostol
My interpretation of these 3 pages is worked out in the attached PDF file. Entirely done in propositional logic language.
Can anyone point out the mistakes or incorrect logical steps (if any) in the attached...
Do you mean if density is not constant, we cannot write:
##\displaystyle\rho=\dfrac{dq}{dV}=\lim_{\Delta V \to 0} \frac{\Delta q}{\Delta V}=\lim_{\Delta V \to 0} \frac{q(V+\Delta V)-q(V)}{\Delta V}##
But this doesn't look analogous to the definition of one dimensional derivative. Consider:
##\dfrac{dy}{dx}=\displaystyle \lim_{\Delta x \to 0} \frac{\Delta y}{\Delta x}=\lim_{\Delta x \to 0} \frac{y(x+\Delta x)-y(x)}{\Delta x}##
There exists only one line segment from origin to each point ##P...
In physics we often come across $$\rho=\dfrac{dq}{dV}$$ Does it mean:
##(i)## ##\displaystyle \lim_{\Delta V \to 0} \dfrac{\Delta q}{\Delta V}##
OR
##(ii)## ##\dfrac{\partial}{\partial z} \left( \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right) \right)##
What does...
I have two volumes ##V## and ##V'## in space such that:
1. ##∄## point ##P## ##\ni## ##[P \in V ∧ P\in V']##
2. ##V## is filled with electric charge ##q##
3. ##\rho = \dfrac{dq}{dV}## varies continuously in ##V##
4. ##V'## is filled with electric charge ##q'##
5. ##\rho' =...
I think I got the solution :
The charge always goes to the outer surface of a conductor. When we connect the two conductors ##A## and ##B## by a conducting wire, the whole system becomes a single conductor.
So the surface of "that" single conductor ##C## will be the surface of the larger...
When I asked "Can we transfer the whole charge of a body to another body?"
my colleague replied:
"If charged body (say 5 Coulomb) is any charged conductor ##A##, it can be done by enclosing ##A## completely by second uncharged conductor ##B## and connecting them by a conducting wire ##B## will...
1) Why does a charged conducting sphere has radially symmetric charge distribution?
2) Or do you mean by placing a charged conducting sphere inside a spherical shell of finite thickness, the shell acquires radially symmetric charge distribution? Why?