A 50 μC charged sphere of mass 0.050 kg is 2.0 m away from a -30 μC charged sphere. The 50 μC
charged sphere is moved at a steady speed to a point 1.2 m away. What is the change in potential
energy of this sphere?
To find the change in potential energy of the sphere, we can use the formula:
ΔU = Ufinal - Uinitial
Where ΔU is the change in potential energy, Ufinal is the final potential energy, and Uinitial is the initial potential energy.
The potential energy of a point charge can be expressed as:
U = k * (q1 * q2) / r
Where U is the potential energy, k is Coulomb's constant (8.99 x 10^9 N·m^2/C^2), q1 and q2 are the charges of the spheres, and r is the distance between the spheres.
First, let's calculate the initial potential energy (Uinitial) of the spheres when they are 2.0 m apart:
Uinitial = (k * (q1 * q2)) / r
Since q1 is 50 μC (50 x 10^-6 C) and q2 is -30 μC (-30 x 10^-6 C), and r is 2.0 m:
Uinitial = (8.99 x 10^9 N·m^2/C^2 * (50 x 10^-6 C) * (-30 x 10^-6 C)) / 2.0 m
Simplifying:
Uinitial = -6748 N·m
Next, let's calculate the final potential energy (Ufinal) when the spheres are 1.2 m apart:
Ufinal = (k * (q1 * q2)) / r
Using the same values for q1 and q2, and r is 1.2 m:
Ufinal = (8.99 x 10^9 N·m^2/C^2 * (50 x 10^-6 C) * (-30 x 10^-6 C)) / 1.2 m
Simplifying:
Ufinal = -16870 N·m
Now we can calculate the change in potential energy (ΔU):
ΔU = Ufinal - Uinitial
= -16870 N·m - (-6748 N·m)
= -16870 N·m + 6748 N·m
= -10122 N·m
Therefore, the change in potential energy of the sphere is -10122 N·m.