What mass of electrons would be required to just neutralize the charge of 4.8 g of protons?
1 answer:
Let's calculate the total charge of M=4.8 g=0.0048 kg of protons.
Each proton has a charge of
, and a mass of 
. So, the number of protons is
And so the total charge of these protons is
So, the neutralize this charge, we must have
electrons such that their total charge is
Since the charge of each electron is
, the number of electrons needed is
which is the same as the number of protons (because proton and electron have same charge magnitude). Since the mass of a single electron is
, the total mass of electrons should be
Each proton has a charge of
So, the neutralize this charge, we must have
Since the charge of each electron is
which is the same as the number of protons (because proton and electron have same charge magnitude). Since the mass of a single electron is
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Part A)
First of all, let's convert the radii of the inner and the outer sphere:
The capacitance of a spherical capacitor which consist of two shells with radius rA and rB is
Then, from the usual relationship between capacitance and voltage, we can find the charge Q on each sphere of the capacitor:
Now, we can find the electric field at any point r located between the two spheres, by using Gauss theorem:
from which
In part A of the problem, we want to find the electric field at r=11.1 cm=0.111 m. Substituting this number into the previous formula, we get
And so, the energy density at r=0.111 m is
Part B) The solution of this part is the same as part A), since we already know the charge of the capacitor:
. We just need to calculate the electric field E at a different value of r: r=16.4 cm=0.164 m, so
And therefore, the energy density at this distance from the center is
First of all, let's convert the radii of the inner and the outer sphere:
The capacitance of a spherical capacitor which consist of two shells with radius rA and rB is
Then, from the usual relationship between capacitance and voltage, we can find the charge Q on each sphere of the capacitor:
Now, we can find the electric field at any point r located between the two spheres, by using Gauss theorem:
from which
In part A of the problem, we want to find the electric field at r=11.1 cm=0.111 m. Substituting this number into the previous formula, we get
And so, the energy density at r=0.111 m is
Part B) The solution of this part is the same as part A), since we already know the charge of the capacitor:
And therefore, the energy density at this distance from the center is