Two small charged spheres are placed so that their centres are 12.5 cm apart. The force of repulsion exerted by one charged sphere on the other is 0.432 N. If the charge on one of the spheres is +2.50 x 10-7 C, then the charge on the other sphere is
Select one:
a. +3.00 x 10-6 C
b. +2.40 x 10-5 C
c. +2.40 x 10-3 C
d. +3.00 x 10-2 C
F = k Q1 Q2 /d^2 (Coulomb's Law)
.432 = 9*10^9 * 2.5*10^-7 Q2/.125^2
Q2 = 3 * 10^-6
To find the charge on the other sphere, we can use Coulomb's law, which states that the force of repulsion between two charged spheres is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers.
The equation for Coulomb's law is:
F = (k * q1 * q2) / r^2
Where:
F is the force of repulsion
k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2)
q1 and q2 are the charges on the two spheres
r is the distance between their centers
In this problem, we are given:
F = 0.432 N
q1 = +2.50 x 10^-7 C
r = 12.5 cm = 0.125 m
k = 9 x 10^9 N m^2/C^2 (constant)
We can rearrange the equation to solve for q2:
q2 = (F * r^2) / (k * q1)
Now we can substitute the given values into the equation:
q2 = (0.432 * (0.125)^2) / (9 * 10^9 * 2.50 x 10^-7)
Calculating this expression will give us the charge on the other sphere (q2).
Using a calculator or performing the calculations, we find that q2 ≈ +2.40 x 10^-5 C.
Therefore, the charge on the other sphere is +2.40 x 10^-5 C.
The correct answer is b. +2.40 x 10^-5 C.