1. A spherical shell with inner and outer radii, a and b respectively, carries a uniform charge with charge density rho_v. a. find the total charge in the shell. b. Use Gauss's Law to find the electric field intensity everywhere in space. c. If a point charge Q is placed at the center of the shell, find the force experienced by the charge Q.

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1. A spherical shell with inner and outer radii, a and b respectively, carries a uniform charge with charge density ρ_v.
   a. Find the total charge in the shell.
   b. Use Gauss's Law to find the electric field intensity everywhere in space.
   c. If a point charge Q is placed at the center of the shell, find the force experienced by the charge Q.

2. Four equal charges are located at the corners of a square of radius a. Assume that the square is in the xy-plane, centered at the origin, and its sides are parallel to the x and y axes.
   a. Find the electric field intensity along the z-axis.
   b. Find the electric potential at any point on the z-axis.
   c. Find the energy in the system of charges.

3. Assume the electric flux density is given by \( D = \frac{2\cos(\theta)}{r^3}a_r + \frac{\sin(\theta)}{r^3}a_\theta \) C/m².
   a. Find the charge density ρ_v.
   b. Find the electric potential V.
   c. Find the energy stored in the spherical region \( r > 3 \) m.
Transcribed Image Text:1. A spherical shell with inner and outer radii, a and b respectively, carries a uniform charge with charge density ρ_v. a. Find the total charge in the shell. b. Use Gauss's Law to find the electric field intensity everywhere in space. c. If a point charge Q is placed at the center of the shell, find the force experienced by the charge Q. 2. Four equal charges are located at the corners of a square of radius a. Assume that the square is in the xy-plane, centered at the origin, and its sides are parallel to the x and y axes. a. Find the electric field intensity along the z-axis. b. Find the electric potential at any point on the z-axis. c. Find the energy in the system of charges. 3. Assume the electric flux density is given by \( D = \frac{2\cos(\theta)}{r^3}a_r + \frac{\sin(\theta)}{r^3}a_\theta \) C/m². a. Find the charge density ρ_v. b. Find the electric potential V. c. Find the energy stored in the spherical region \( r > 3 \) m.
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