earnshows theorem?`?

Question

earnshows theorem says that no particle can b in stable equilibrium under the action of electrostatic force alone. consider ,however, a positive point charge at the center of a square of four equal positive charges ,this point charge seems to b in stable equilibrium as all the four charges push it towards the center ,yet earnshows theorem holds,,, can u explain how?

Answer 1

Earnshaw's theorem applies to 3-dimensional (i.e., real) space.

What you showed is that the positive point particle is stable IF the particle is somehow confined to the plane: then it's true that every little step away from the center will result in a push back.

But let the point charge step upwards out of the plane of the square, and now you find that all the charges at the corners are contributing to a force that pushes the point charge even further out of the plane.

So that equilibrium point in the center is not stable against vertical motion, out of the plane.

Answer 2

Equilibrium means that there is no net force on the object. Stability means that *any* slight displacement from the equilibrium position will result in forces that push the object back into equilibrium (like a ball a the bottom of a hill). In your example, a slight displacement out of the plane of the square will cause the center charge to accelerate away from the center. That means the equilibrium is unstable.

Answer 3

i think of you mean (Amalie) Emmy Noether; Albert Einstein reported she replaced into the main influential woman in arithmetic. Her theorem states that any differentiable symmetry of the action of a actual device has a corresponding conservation regulation.