901 LTE A 45 cm diameter conducting sphere is charged to 700

9:01 LTE A 45 cm -diameter conducting sphere is charged to 700 V relative to V-0 at r-o? Part A What is the surface charge density ? Express your answer using two significant figures in C/m 2 Part B At what distance from the center of the sphere will the potential due to the sphere be only 24 V? Express your answer using two significant figures in

Solution

Part A

Let the charge on the conductor be Q

Potential at surface of sphere = kQ/r = 9*10⁹*Q/0.225=700

Q=(700*0.225)/(9*10⁹)=17.5*10^-9 C

Surface area of sphere = 4*pi*0.225²=0.636 m²

Surface charge density = (17.5*10^-9)/0.636 = 27.5*10^-9 C/m²

Part B:

Let the distance at which potential=24 V be r from center of sphere

9*10⁹*17.5*10^-9/r=24

r=6.56m

Answer is 6.56 meters