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.
I KNOW r=Kcx q1xq2/PE
But I tried using the charge of an electron -1.6E-19 for both q1 and q2, yet I still get the incorrect answer...
but there is more than one electron, there are 1E13 electrons per sphere.
I tried using 1E13 as q1 and -1.6E-19 as q2, and I still got it wrong...
You're stupid.. -_-
-1.6E-19 times 1E13 = q1 and q2
((8.98755x10^9)(q1)(q2))/-0.061J = the answer...
To find the distance between the two spheres, you can use the formula you mentioned:
r = K * (|q1| * |q2|) / PE
Where:
- r is the distance between the two spheres (in meters)
- K is the Coulomb constant (8.98755 × 10^9 N·m^2/C^2)
- q1 and q2 are the charges on the two spheres (in Coulombs)
- PE is the electrical potential energy associated with the two spheres (in Joules)
In this case, one metal sphere has lost electrons, so it has a positive charge, and the other sphere has gained electrons, so it has a negative charge. The charge on an electron is 1.6 × 10^-19 C, as you mentioned.
Let's calculate the charges on the two spheres:
- The first sphere lost 1 × 10^13 electrons, so its charge is q1 = -1.6 × 10^-19 C * 1 × 10^13 = -1.6 × 10^-19 C * 1 × 10^13 = -1.6 × 10^-6 C
- The second sphere gained 1 × 10^13 electrons, so its charge is q2 = -(-1.6 × 10^-19 C * 1 × 10^13) = 1.6 × 10^-6 C
Now, substitute the values into the formula:
r = (8.98755 × 10^9 N·m^2/C^2) * (|-1.6 × 10^-6 C| * |1.6 × 10^-6 C|) / (-0.061 J)
Note that we take the absolute values of the charges since the formula only requires the magnitudes.
Evaluate the expression:
r = (8.98755 × 10^9 N·m^2/C^2) * (1.6 × 10^-6 C * 1.6 × 10^-6 C) / (-0.061 J)
Now, calculate:
r = (8.98755 × 10^9 N·m^2/C^2 * (2.56 × 10^-12 C^2) / (-0.061 J)
Simplify:
r = (8.98755 × 10^9 N·m^2 * 2.56 × 10^-12 C^2) / (-0.061 J)
Next, convert the units to the appropriate SI unit:
r = (8.98755 × 10^9 kg·m^3/s^2 * 2.56 × 10^-12 C^2) / (-0.061 kg·m^2/s^2)
Simplify further:
r = - (8.98755 × 10^9 kg·m^3 * 2.56 × 10^-12 C^2) / (0.061 kg·m^2)
Finally, calculate the value:
r = - 3.866485 × 10^-4 m
The distance between the two spheres is approximately -3.866485 × 10^-4 meters. Note that the negative sign indicates that the spheres are attracted to each other.