A metal sphere has a charge of +7.80μC. What is the net charge after 5.97E+13 electrons have been added to it?
charge= e*numbercharge
original number of electron deficincy on sphere: n=7.8E-6 * e where e is the charge on a single electron.
now add the charges (remember the charge on electrons is negative), so the net is the electron (extra or deficiency) on the sphere, convert that then to coulombs.
To calculate the net charge after adding electrons to a metal sphere, we need to understand that adding electrons to an object increases its negative charge.
First, let's determine the charge of a single electron. The elementary charge, denoted as e, is approximately -1.602 × 10^-19 coulombs (C).
Next, we can calculate the total charge added to the metal sphere by multiplying the number of electrons added by the charge of a single electron. In this case, the number of electrons added is 5.97 × 10^13, and the charge of a single electron is -1.602 × 10^-19 C.
Total charge added = (5.97 × 10^13 electrons) × (-1.602 × 10^-19 C)
To find the net charge, we will add the initial charge of the metal sphere (+7.80 μC) to the total charge added.
Net charge = Initial charge + Total charge added
Now, let's convert the initial charge of the metal sphere from microcoulombs (μC) to coulombs (C).
1 microcoulomb (μC) = 1 × 10^-6 coulombs (C)
So, the initial charge of the metal sphere is 7.80 μC = 7.80 × 10^-6 C.
Substituting the values into the equation:
Net charge = 7.80 × 10^-6 C + (5.97 × 10^13 electrons) × (-1.602 × 10^-19 C)
Now you can calculate the net charge by performing the arithmetic.