# Turning Pull Into Push?

It's textbook physics: An electric charge near the surface of a material gets pulled toward the surface. However, if the charge is spread out into the right shape and moves fast enough, that attraction becomes a repulsion, one physicist calculates. The odd finding could help physicists avoid unexpected effects when guiding beams of particles such as electrons.

"At first I thought this was completely wrong, but when you think about the situation, it's not," says Primož Rebernik Ribič, a physicist at the Swiss Federal Institute of Technology in Lausanne, who presents his calculation online today in Physical Review Letters. However, not everybody agrees that his analysis is correct.

Suppose a "point charge," such as a single electron, is hovering above a surface of a conductor. The electric field from the charge pulls and pushes other free-moving charges in the surface. So those charges rearrange themselves in a way that causes the point charge and the surface to attract each other. In fact, the force equals the one that would be created by an opposite "image charge" lurking as far below the surface as the original charge hovers above it—the textbook example. In an insulator, things are slightly more complicated. The positive and negative charges in the material can only shift their positions a bit to polarize the material. Still, the point charge induces a pattern of polarization that attracts it to the surface.

However, if the point charge is replaced with a rodlike line of charges that moves sideways—like a knife spreading peanut butter—then the force from the surface can become repulsive, Rebernik Ribič argues.

To see how this scenario works, consider the case in which just a point charge moves across the surface of an insulator. In that case, the polarization pattern moves with it, becoming so-called evanescent waves that still attract the point charge.

If the point charge moves fast enough, another factor comes into play. In an insulating material such as glass, light travels slower than in empty space. And if a charge moves through the glass faster than light can, it creates a shockwave of light, known as Cherenkov radiation, much like the sonic boom from a supersonic jet. Now, if a point charge above the insulator whizzes along faster than light can within the material, then the induced polarization pattern will move that fast as well and create Cherenkov radiation. That radiation flows at an angle down into the material and carries momentum with it. But by Newton's law that every action has an equal and opposite reaction, the downward flow of momentum must be balanced by an upward push on the point charge.

For a moving point charge, the pull of the evanescent waves always swamps the push of the Cherenkov radiation, Rebernik Ribič calculates. When a line of charge moves across the surface, however, the evanescent waves created by different points along the line interfere with one another in a way that cancels out the attraction from them. The repulsion from the Cherenkov radiation remains, leaving an overall push upward on the line of charge. The same thing holds for a conductor, Rebernik Ribič calculates.

Not everybody is convinced. Levi Schächter, a physicist at the Technion-Israel Institute of Technology in Haifa, says his own calculations for a line of charge show the net force remains attractive. "So at the bottom line, I believe Dr. Rebernik Ribič is wrong," he says. However, Georg Hoffstaetter, an accelerator physicist at Cornell University, says he finds Rebernik Ribič's argument plausible.

If it's right, what might the odd repulsion be good for? That's not clear. If researchers want to repel fast-moving bunches of electrons from a surface, they can do it more easily by charging the surface than by shaping the bunches, Hoffstaetter notes. On the other hand, he says, knowing that this unwanted nudge could crop up might help physicists avoid problems when designing an apparatus to handle beams of charged particles. And the odd effect could find unexpected uses, Hoffstaetter says: "Sometimes effects like these start out as nuisances but people come to love them."

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