question_answer

Two copper spheres having same radii, one solid and other hollow, are charged to the same potential. Which of the following statements is correct?

A)  Hollow sphere will hold more charge

B)  Solid sphere will hold more charge

C)  Solid sphere will have uniform volume charge density

D)  Both spheres will hold same charge-

Correct Answer: D

Solution :

Capacitance of the solid sphere \[=4\pi {{\varepsilon }_{0}}\,R\] where, R is radius of .the sphere. Capacitance of the hollow sphere \[=4\pi {{\varepsilon }_{0}}\,R\] Charge on the solid sphere \[=({{C}_{sould}})V=(4\pi {{\varepsilon }_{0}}R)(V)\] Charge on the hollow sphere \[=({{C}_{hollow}})\,\,(V)\] \[=(4\pi {{\varepsilon }_{0}}\,R)\,\,(V)\] \[\Rightarrow \] \[{{C}_{soild}}={{C}_{hollow}}\] Thus, both spheres will hold same charge.