At a separation distance of 0.500-m, two like-charged balloons experience a repulsive force of 0.320 N. If the distance is tripled, then the

Hi Alan,

I was just thinking about this.

If you put one of the balloons at the centre of a sphere with a radius of r units.  

Then for that sphere  the        $$Surface \;area=4\pi r^2$$

The attractive force will be the same for every point on the surface of that sphere.

Now

It is a concentic sphere encases the first one and it has a radius of  3r then

For this second sphere    

    $$\\Surface \;area=4\pi (3r)^2=4\pi*9r^2=9*(4\pi r^2) \\= 9*$ the original spheres surface area$\\\\$$

So the force would have to be 9 times less if the radius is 3 times more.  

Does that make sense Alan?

Electrostatic force is inversely proportional to the square of the distance between the two balloons, so if this distance is tripled the force will be 9 times smaller, namely:   0.32/9 N

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