Define voltage specifically what does it mean to say that

Question

Question 1.

(a) Define voltage. Specifically, what does it mean to say that the voltage between two points is +25 volts?

(b) An electric scalar potential V is given by V(x, y, z) = -3x²yz. Calculate the electric field from this potential. Show that this electric field is conservative. Show Work!

Question 2. A charge of Q₁ =10^-3 Coulombs is located at (2, 0) and a charge of Q₂ = 2 x 10^-3 Coulombs is located at (-4,0). (Note: Co = 8.854 x 10^-12 F/m.)

(a) Including units, what is the total electric energy in the field of these two charges?

(b) Including units, calculate the potential at point (0,0). How much work (in joules) is required to bring a charge of Q = 10^-3 Coulombs from oo to point(0, 0)? Assume the potential V(∞) = 0.

Question 3.

(a) Calculate the potential at point P located a distance z above the center of a charged disk of radius a and surface charge density p. Coulombs per square meter. Please show all work. An integral that you may need is

∫ΡdΡ/(√(Ρ² + z²)) = √(Ρ² + z²)

The elemental area in cylindrical coordinates is dA = ΡdΡdΦm².

(b) Calculate the electric field at P. Use back of page if necessary.

Question 4. A charge +Q is located at the center of a shell of dielectric (inner radius r₁ and outer radius r₂) with a dielectric constant ∈_r. Inside and outside of the shell is free space. Plot the electric field E^→, the electric flux density D^→, and the polarization P in the three regions 0 < r < r₁,r₁ < r < r₂ and r > r_2.

Question 5. A parallel place capacitor has an equivalent plate area of A = 2 m² and is charged to 20 volts. The dielectric has a permittivity of er = 12 and a plate separation of d = 0.0002 m. Include units in all answers. (Note: eo = 8.854 x 10^-12 F/m.)

(a) Calculate the capacitance C.

(b) Calculate the total charge Q stored on the capacitor.

(c) Calculate the surface charge density on the plates, Ρ_s.

(d) Calculate the electric field E between the plates of the capacitor.

(e) From E, calculate the electric displacement D in the dielectric.

(f) Calculate the electric susceptibility xE of the dielectric.

(g) Calculate the electric polarization P in the dielectric.

(h) Calculate the total energy stored in the capacitor.

(i) Briefly and dearly explain the physical significance of the dielectric constant ∈_r. For example, what is the difference between a material with a dielectric constant ∈_r = 12 and a material with dielectric constant ∈_r = 5?