a solid copper sphere 10 mm in diameter has a positive charge arising from the removal of one electron from each 10^12 copper atoms. determine the net charge on the sphere, the electric field strength and electric potential at the surface.
To determine the net charge on the sphere, we need to calculate the total number of electrons removed from the copper atoms.
Given that there is one electron removed from each 10^12 copper atoms, we can calculate the total number of electrons removed by dividing the number of copper atoms in the sphere's volume by the ratio of removed electrons per copper atom.
The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius of the sphere. In this case, the diameter of the sphere is 10 mm, so the radius is half of that, which is 5 mm or 0.005 m.
Substituting the values, V = (4/3) * π * (0.005)^3.
Next, we need to calculate the total number of copper atoms in the sphere. The number of copper atoms is given by Avogadro's number, which is approximately 6.022 × 10^23 atoms per mole. So, to find the number of copper atoms in the sphere, we divide the volume of the sphere by the atomic volume of copper.
The atomic volume of copper is the molar volume of copper divided by Avogadro's number. The molar volume of copper is approximately 7.11 × 10^6 m^3/mol.
Substituting the values, the atomic volume of copper = (7.11 × 10^6) / (6.022 × 10^23).
Now, we can calculate the total number of copper atoms in the sphere by dividing the volume of the sphere by the atomic volume of copper.
The total number of copper atoms in the sphere = V / (atomic volume of copper).
Now we need to calculate the number of removed electrons. Since there is one electron removed from each 10^12 copper atoms, the number of removed electrons = (total number of copper atoms in the sphere) / (10^12).
Finally, the net charge on the sphere is equal to the number of removed electrons.
To determine the electric field strength at the surface, we can use the formula:
E = k * (q / r^2),
where E is the electric field strength, k is the electrostatic constant (approximately 8.99 × 10^9 Nm^2/C^2), q is the net charge on the sphere, and r is the radius of the sphere.
Substituting the values, E = (8.99 × 10^9) * (charge on the sphere) / (radius of the sphere)^2.
To determine the electric potential at the surface, we can use the formula:
V = k * (q / r),
where V is the electric potential, k is the electrostatic constant, q is the net charge on the sphere, and r is the radius of the sphere.
Substituting the values, V = (8.99 × 10^9) * (charge on the sphere) / (radius of the sphere).
By calculating these values using the given information, you can determine the net charge on the sphere, the electric field strength, and the electric potential at the surface.