Initially, both metal spheres are neutral.
In a charging process, 1 × 1013 electrons are
removed from one metal sphere and placed on
a second sphere. Then the electrical poten-
tial energy associated with the two spheres is
found to be −0.061 J .
The Coulomb constant is 8.98755 ×
109 N · m2/C2 and the charge on an electron
is 1.6 × 10−19 C.
What is the distance between the two
spheres?
Answer in units of m.
energy= kQ^2/r
solve for r
To find the distance between the two spheres, we can use the formula for electrical potential energy between two point charges:
U = (k * |q1 * q2|) / r
where U is the electrical potential energy, k is the Coulomb constant, q1 and q2 are the charges on the two spheres, and r is the distance between them.
In this case, we know the electrical potential energy (U = -0.061 J), the Coulomb constant (k = 8.98755 x 10^9 N · m^2/C^2), and the charge on an electron (q = 1.6 x 10^-19 C). However, we need to determine the charges on the two spheres.
The number of electrons removed from one sphere is given as 1 x 10^13. We know that the charge on a single electron is -1.6 x 10^-19 C, so the total charge removed from the first sphere is:
q1 = (1 x 10^13) * (-1.6 x 10^-19 C)
Next, we know that these electrons were placed on the second sphere, so the charge on the second sphere is:
q2 = (1 x 10^13) * (1.6 x 10^-19 C)
Now we can substitute the values into the formula for electrical potential energy and solve for the distance (r):
-0.061 J = (8.98755 x 10^9 N · m^2 / C^2) * (|q1 * q2|) / r
Substituting the values of q1, q2, and rearranging the equation gives:
r = (|q1 * q2|) / (8.98755 x 10^9 N · m^2 / C^2 * (-0.061 J))
Calculating the values gives:
q1 = (1 x 10^13) * (-1.6 x 10^-19 C) = -1.6 x 10^-6 C
q2 = (1 x 10^13) * (1.6 x 10^-19 C) = 1.6 x 10^-6 C
r = (|-1.6 x 10^-6 C * 1.6 x 10^-6 C|) / (8.98755 x 10^9 N · m^2 / C^2 * (-0.061 J))
Simplifying the calculation gives:
r = (2.56 x 10^-12 C^2) / (-5.4883 x 10^8 N · m^2)
Now we can plug in the values and calculate the distance (r).