Question about this Concept about Coulomb's Law

[aeromat]

Homework Statement

Strictly speaking, the description of Coulomb's law given on the previous page (written below this paragraph) is meant to apply to point charges. However, just as Newton was able to develop the mathematics(calculus) that proved the mass of any spherical object can be considered to be concentrated at a point at the centre of the sphere for all locations outside of the sphere, so it might also be proven that if charge is uniformly distributed over the surface of a sphere, then the value of the charge can be considered to be acting at the centre for all locations outside the sphere.

I got confused with the bolded portion. Would anyone mind elaborating on what they are trying to say here?

The description of Coulomb's Law (from the textbook): The electrostatic force between two point charges, q₁ and q₂, distance r apart, is directly proportional to the magnitudes of the charges and inversely proportional to the square of the distance between their centres.

 

[Doc Al]

I got confused with the bolded portion. Would anyone mind elaborating on what they are trying to say here?

If you have an amount of charge (Q, say) spread out uniformly on the surface of a sphere (of radius R, say), then the field from that surface charge (for distances > R) is the same as that of a point charge Q placed at the center of that sphere.

Does that help?

 

[aeromat]

Would you mind giving me any real-life examples that explain this concept?

 

[ideasrule]

I have a big 2m ball with 8uC of charge, uniformly distributed throughout its volume, with its center at x=0, y=0, z=0. If I destroy the ball and put a point charge at (0,0,0) with magnitude 8uC, the electric field will be exactly the same at every point except the points that used to be inside the sphere.

 

[rwisz]

I can understand your confusion with the bolded portion. Essentially, what it is saying is that Coulomb's Law is typically used to calculate the electrostatic force between two point charges. However, if the charge is distributed over the surface of a sphere, the mathematics can be adjusted so that the charge can be considered to be acting at the center of the sphere. This is similar to how Newton's equations can be applied to objects of different shapes and sizes by considering their mass to be concentrated at a single point. In summary, the bolded portion is just explaining an additional application of Coulomb's Law for charges distributed over a spherical surface.