A Field of Fixed Charges in a Vacuum 24.1. Estimate the upper limit of the error made in calculating the force of interaction between charged spherical conductors with the aid of the Coulomb law. The radii of the spheres are ro, the distance between their centres is r. Carry out the calculations for `r ge20 r_(0)`.

Explanation

It is evident from Fig. 24.1 for the case of charges of different signs that the actual force of interaction of the charges is greater than it would have been, if the charges were concentrated in the centres of the spheres, and less than if the charges were concontrated at the nearest points of the spheres:

`(q^(2))/(4pi epsi_(0)r^(2)) lt F lt (q^(2))/(4pi epsi_(0)(r-2r_(0))^(2))`
The absolute error is less than the difference between the bounding values, the relative error being less than the ratio of this difference

to the minimum, force. Hence
`epsi lt (F_(2)-F_(1))/(F_(1))=(r^(2)-(r-2r_(0))^(2))/((r-2r_(0))^(2))=(4r_(0)(r-r_(0)))/((r-2r_(0))^(2))`