Problem 0

Contributed by Johanes Suhardjo (Indonesia/Hong Kong University of Science and Technology).

Anyone is welcome to submit the solution of this problem. Best solutions will be published together with the names, but no marks will be added to the score of Physics Cup 2020. One hint will be published, though, on 15th November. This problem could have easily been Problem No 1, but unfortunately there are some students who can possibly participate and already know the problem.

The resistivity of thin homogeneous isotropic electrically conducting sheets is usually characterized by the sheet resistance, here denoted as \rho , which is the resistance between the opposing ends of a square-shaped sheet.

Consider a very wide sheet of sheet resistance \rho . Two small electrodes are
put on the sheet at points A and B , a distance s\equiv |AB| apart. The resistance between these electrodes is measured to be R_1 . The sheet is then cut to become a circle of radius r centered at a point O so that \angle AOB=\theta and |OA|=|OB|<r. Denoting the new resistance between the two electrodes by R_2 , find the resistance change \Delta \equiv R_2-R_1 .

Translation into Chinese

The hint for Problem 0