Can anybody help me solve this problem? Thank you so much!
1 answer:
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Answer:
a) 0 < r < R: E = 0, R < r < 2R: E = KQ/r^2, r > 2R: E = 2KQ/r^2
b) See the picture
Explanation:
We can use Gauss's law to find the electric field in all the regions:
EA = qen/e0 where qen is the enclosed charge
Remember that the electric field everywhere outside a sphere is:
E(r) = q/(4*pi*eo*r^2) = Kq/r^2
a)
- For 0 < r < R: There is not enclosed charge because all of it remains on the outer layer of the conducting sphere, therefore E = 0 EA = 0/e0 = 0 E = 0
- For R < r < 2R: Here the enclosed charge is equal Q E = Q/(4*pi*eo*r^2) = KQ/r^2
- For r > 2R: Here the enclosed charge is equal 2Q E = Q/(4*pi*eo*r^2) + Q/(4*pi*eo*r^2) = 2Q/(4*pi*eo*r^2) = 2KQ/r^2
b) At the beginning there is no electric field this is why you see a line in zero, In R the electric field is maximum and then it starts to decrease exponentially with the distance and finally in 2R the field increase a little due to the second sphere to then continue decreasing exponentially with the distance
a) the number of protons is more than the electrons
b)
Explanation:
The net electric charge on the ball is
This electric charge is given by the algebraic sum of the charge of the protons and of the charge of the electrons.
The charge of one proton is:
While the charge of one electron is
So the net charge on the metal ball will be given by
where
is the number of protons
is the number of electrons
So we find:
This means that the number of protons is more than the electrons.
b)
In this case, we want to make the ball neautral, so we have to remove a net charge of Q' such that the new charge is zero:
This implies that the charge that we must remove is
To do that (and to make the ball losing mass at the same time), we have to remove protons, since they have positive charge.
The number of protons that must be removed is:
The mass of one proton is
Therefore, the total mass that must be removed from the ball is