Let z < 0 be region 1 with dielectric constant &r1 = 4, while z > 0 is region 2 with &r2 = 7.5. 60a, 100a, + 40a, V/m, Calculate D₂. Given that E₁ (Hint: Boundary conditions) =

The electric potential of a charged conducting sphere (as well as a spherical shell) can be calculated as Q R' V = k where is the charge and R is the radius of the sphere. Calculate the electric potential of a solid conducting sphere of a radius of R = 6 cm if the sphere loses 0.1% from the total number of its free electrons. The sphere is made of aluminum and has the density 2.7 g/cm³, molar mass 27 g/mol and one free electron per atom. Follow the steps listed below. 1. Find the number of free electrons per cm³ in aluminum. The number of free electrons per cm³, ne = Units Select an answer ✓ 2. Calculate the volume of the sphere and use it to find the total number of free electron inside the sphere. The number of free electrons, Ne = Units Select an answer 3. Calculate the charge of the sphere after it loses 0.1% of its electrons and use it to find the potential of the sphere. The electric potential of the sphere, V = Units Select an answer ✓

Question 3. Using the general expression V(r,0) = Eo (A,r +) P.(cos0) for the potential at a %3D distance r from the center of a sphere shell of radius R. The acceptable expressions for potentials inside and outside the shell are: V(r,e) E, A,r' P;(cos®) (rSR) and V (r,0) = Eo P.(cose) (r2 R) %3D A constant charge density oo is ghed over the surface of the shell Determine the potential inside and outside the shell for this charge distribution

A charged conducting spherical shell of radius R = 3 m with total charge q = 23 μC produces the electric field given by E⃗ (r)={014πϵ0qr2r̂ forforr<Rr>R(PICTURE ATTACHED OF EQUATION) a. Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity.  V(r)= b. Calculate the electric potential, in volts, at radius r inside the charged shell. V(r) =