Several solid conducting spheres of different radii are all connected to a common high-voltage generator such that they acquire the same electrostatic potential. Which of the following curves best represents the variation of surface charge density ( ) of the spheres with their radius ( r )?

Step-by-step solution

When the conducting spheres are connected to a common high-voltage generator, they all acquire the same electrostatic potential V . The electric potential at the surface of a conducting sphere of radius r and charge q is given by: V = 1 4 ₀ q r The surface charge density is the charge per unit area: = q 4 r^2 q = (4 r^2) Substituting q into the potential equation: V = 1 4 ₀ (4 r^2) r = r ₀ Rearranging for surface charge density: = ₀ V r Since the potential V is constant for all spheres, the surface charge density i