Electrostatics: Potential of +28.0 nC Sphere in Vacuum

[NegaChin]

A 2.00 mm diameter conducting sphere in vacuum is charged with +28.0 nC. Determine the potential at a distance of 1.70 m from its center. [Hint: Since 1.70 m >> 2.00 mm this is essentially a point-charge.]

 

[hage567]

Please show what you've tried so far.

 

[Moetasim]

I can say that the potential at a distance of 1.70 m from the center of a +28.0 nC sphere in vacuum can be calculated using the equation V = kQ/r, where V is the potential, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere.

Plugging in the values, we get V = (9 x 10^9 Nm^2/C^2)(28.0 x 10^-9 C)/1.70 m = 147.1 V.

This means that at a distance of 1.70 m from the center of the sphere, the potential is 147.1 volts. This is a significant amount of potential and shows the strong electrostatic force exerted by the charged sphere.

Furthermore, since the distance is much larger than the diameter of the sphere, we can treat the sphere as a point charge, which simplifies the calculation. This also shows the importance of understanding the concept of point charges in electrostatics.

In conclusion, the potential at a distance of 1.70 m from a +28.0 nC sphere in vacuum is 147.1 V, calculated using the equation V = kQ/r. This knowledge can be useful in understanding the behavior of charged particles and the forces they exert in electrostatics.