Question

You have a hollow conducting sphere of radius 5 cm. the electric field at 10 cm measured radially outward from the center of the sphere is 8.99x1046 2. N/C. a. b. c. d. What is the charge of the sphere? What is the surface charge density of the sphere? What is the electric field at a distance r-1 cm from the center of the sphere? What is the potential at the center of the sphere? R-5 cm R-10 cm

Answer 1

Radius of the conducting sphere is R = 5 cm = 0.05 m part-a consider a spherical Gaussian surface of radius r (r > R). According to Gauss's laws contourintegral E.dA = 1/epsilon_0 Q_ene [Q_ene = charge enclosed by the surface. From symmetry E.dA = E daA therefore E contourintegral dA = 1/epsilon_0 Q_ene implies E times 4 pi r^2 = 1/epsilon_0 Q [contour dA = surface area of the Gaussian sphere = 4 pi r^2 Q_ene = charge on the sphere = Q(say)] implies E = Q/4 pi epsilon_0 r^2 - (i) (r > R) Mass at r = 10 cm = 0.1 m, E = 8.99 times 10^6 N/e using this and epsilon_0 = 8.85 times 10^- 12 F/m we get from eq - (1) Q = 4 pi epsilon_0 r^2 times E = 4 pi times 8.85 times 10^- 12 times (0.1)^2 times 8.99 times 10^- 6 e = 1.00 times 10^- 5 e So charge of the sphere is