Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A metal ball of radius cm is charged in dry air. Air breaks down and sparks when the field passes V/m. Find the greatest charge the ball can hold, and its potential at that moment. Take .
In a conductor at rest the field inside is zero and the extra charge sits on the surface. Just outside, , with . A ball of radius with charge has the potential and the field at its surface, with . Joined spheres share the charge in the ratio of the radii. In a dielectric and the bound charge has .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. m, V/m.
Plan. The field is strongest at the surface. The ball sparks when that field reaches .
Step 1. The charge. , so , that is .
Step 2. The potential. , that is kV.
Answer: and kV.
Check. , and . It fits.
What if? A ball of half the radius holds a quarter of the charge before it sparks, since . A sharp point sparks at a much lower potential.
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