Question

You are given the following field distribution (please note the change in the problem: in region 4 A

Region 1 rhoRegion 2 aRegion 3 bRegion 4 cExamine the boundary conditions at rho=a,rho=b,rho=c

Answer 1

To examine the boundary conditions at ρ=a, ρ=b, and ρ=c, we need to determine the electric potential in the given regions. The electric potential in these regions can be found using the equation V = -∫E・dr, where V is the electric potential, E is the electric field, and dr is the displacement vector.

Step-by-step explanation:

To examine the boundary conditions at ρ=a, ρ=b, and ρ=c, we need to determine the electric potential in the given regions. The electric potential in these regions can be found using the equation V = -∫E・dr, where V is the electric potential, E is the electric field, and dr is the displacement vector. Since the electric field is given by E = PR²/(2ε₀r), we can substitute this expression into the integral and solve for each region.

(a) For ρ

(b) For R₁<ρ

(c) For ρ>R₂, the electric field expression remains E = PR²/(2ε₀r). We can evaluate -∫E・dr from ρ=R₂ to ρ=∞ to find the electric potential.