Analytical Expression of Ampere’s Force Between Two Current Rings in a Compensated Torsion Balance

An analytical expression of ampere’s force between two current rings in a compensated torsion balance is deduced here,the properties and stability of this force are discussed.The result of numerical estimation for typical experimental parameters shows that the uncertainties of the force are smaller than 1×10^(-4) orders,which is very important for precise measurement of gravitational constant G.