A disk of radius R has positive charge uniformly distributed over an inner circular region of radius a and negative charge uniformly distributed over the outer annular (ring-shaped) region . The surface charge density on the inner region is +σ, and that on the annular region is −σ. The electrostatic potential at P, located on the central perpendicular axis a distance z=R from the disk center, is zero.

What is a?

Express your answer in terms of R. Express the coefficients using three significant digits.

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?