News in Science

Maths shows balls with like charge attract

Surprising attraction Contrary to what most people think, two positively-charged metal spheres that get close enough will almost always attract, according to a New Zealand physicist.

Professor John Lekner of Victoria University of Wellington describes his mathematical proof today in Proceedings of the Royal Society A.

"It's very ingrained in us that like charges repel and so how could this possibly happen?" says Lekner.

"Some colleagues and referees accepted it immediately and others were very resistant to the idea."

While most people learn in school that opposite charges attract and like charges repel, Lekner says when it comes to metal spheres, like charges don't always repel.

He developed a model that describes what happens when two positively-charged conducting spheres are placed at various distances between them.

"If they get close together they can attract even though both have a net positive charge," says Lekner.

"You get this effect when the spacing between the spheres is small relative to size of the spheres."

Mobile electrons

Lekner says because electrons are completely mobile in a conducting sphere, they are able to move to create negative and positive poles on the spheres.

The positive pole of one sphere can then attract the negative pole of the other.

Lekner says the same effect is likely to occur in conductors of different shapes but he chose spheres because the effect can be described by a relatively simple mathematical formula.

The findings may explain a number of puzzling observations, including one dating back to 1836 when a researcher by the name of Snow Harris found attraction between two metallic objects with like charge.

"There are a lot of instances where people have found specific cases of attraction at close quarters," says Lekner.

"But I was surprised to find a general theorem - it was a gift from nature."

Exception

Lekner says there is only one circumstance under which spheres with like charges repel at close quarters.

This is when the ratio of charges on the two spheres is the same as it would be if the spheres had made contact and charge was able to flow between them to give each sphere the same voltage.

If the two spheres have this equal voltage, they will repel each other at all distances, says Lekner.

He says the findings could be relevant to other situations where charge separation and static electricity occurs, such as those involving droplets in clouds, or carbon particles in flames.