Question

Physics 2, unit: Electrostatics. Please answer all

A spherical insulator with a radius 1.0 m and a charge density of -9 uC/m2 distributed uniformly throughout. Concentric to this sphere is a hollow, uncharged, metallic sphere of inner radius 2 m and outer radius of 3 m. Find the electric field at the radii r-0.8 m, and r-2.5m. What is the charge on the outside surface of the outer sphere? 2 m 3 m For a region in space, the electric potential is described by the relationship: V(x,y,z)-4xyz +5xz2 +7yz, with V in volts and x, y, z in meters Find the electric field at the point (2 m, 3 m, 4 m) Four capacitors are connected as shown. Find the total capacitance of the system. Ifa total of 20 volts is applied to the ends, what would the total energy stored in the circuit be, and what is the charge on each capacitor? 3 F 8F 4F

Answer 1

For determines the electric field inside of a uniformly charged sphere of Radius R and change density rho Consider a Gaussian surface at a radius 'r' Using symmetry Let the electric field at r be E. Using Gaussian law, contourintegral E^rightarrow middot ds^rightarrow = Q/elemeof_0, Q = rho middot 4/3 pi r^2 implies E. pi r^2 = 1/elementof_0 rho middot 4 pi/3 r^3 implies E = 1/elementof_0 rho/3 r = rho r/elementof_0 Now rho = -9 mu c/m^3 r = 0.8 m therefore E = -9 times 10^-6 times 0.8/3 times elementof_0 = -2.4 times 10^-6/8.85 times 10^-12 = -0.2712 times 10^6 N/c. therefore E^rightarrow = -0.2712 times 10^6 r^cap N/c. For r = 2.5 cm it is inside the metallic conduction we know for metallic conductor E = 0 Let assume the total charges of the sphere Q = 4/3 pi rho R^3 consider a Gaussian surface of radius r (R_1 < r < R_2) it is inside the metal.
the charge on 6F capacitor and 3F capacitor= 22.86 C and on 4F capacitor = 45.72 C and on 8F capacitor = 68.57 C