What is meaning of charge?
2 answers:
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Answer:
at r < R;
at 2R > r > R;
at r >= 2R
Explanation:
Since we have a spherically symmetric system of charged bodies, the best approach is to use Guass' Theorem which is given by,
(integral over a closed surface)
where,
= Electric field
= charged enclosed within the closed surface
= permittivity of free space
Now, looking at the system we can say that a sphere(concentric with the conducting and non-conducting spheres) would be the best choice of a Gaussian surface. Let the radius of the sphere be r .
at r < R,
= 0 and hence
= 0 (since the sphere is conducting, all the charges get repelled towards the surface)
at 2R > r > R,
= Q,
therefore,
(Since the system is spherically symmetric, E is constant at any given r and so we have taken it out of the integral. Also, the surface integral of a sphere gives us the area of a sphere which is equal to )
or,
at r >= 2R
= 2Q
Hence, by similar calculations, we get,
When the iron and the water reach thermal equilibrium, they have same temperature, 
.
We can consider this as an isolated system, so the heat released by the water is equal to the heat absorbed by the iron.
The hear released by the water is:
where
is the water mass, 
is the specific heat of the water, and 
is the variation of temperature of the water.
Similarly, the heat absorbed by the iron is:
where
is the iron mass, 
is the iron specific heat, and 
is the variation of temperature of the iron.
Writing
and replacing the numbers, we can solve to find mw, the mass of the water:
We can consider this as an isolated system, so the heat released by the water is equal to the heat absorbed by the iron.
The hear released by the water is:
where
Similarly, the heat absorbed by the iron is:
where
Writing