Each plate of an ideal air-filled parallel-plate capacitor has an area of 1,424 mm² and the separation of the plates is 0.076 mm. An electric field of 2.610 x 106 V/m is present between the plates. What is the surface charge density on the plates? (o = 8.85 x 10-12 C²/N·m²) Give your answer in µC/m².

Ra1 +9 -9 Rea Consider two concentric spherical conductors, separated by an isolating material with (absolute) permittivity e. The two conductors have radius R1 and R2, they are put on a potential V and V2, which leads to a charge +q and –q sitting on them, respectively. By the problem's spherical symmetry, we see that the charge on each conductor is distributed uniformly, and that, in spherical coordinates, the electric field between the two conductors is of the form E(r) = -E(r) er. Determine the capacity C using the following steps: 1. Use Gauss's Law in integral form, with N a ball of radius r (R2 < r < R1), to find an expression for E(r) in terms of q. 2. Calculate AV = Vị – V2 using the formula - E•dr Δν and with C the black line segment indicated on the drawing (parallel with e,). 3. The capacity now follows from C = q/AV.

The electric field strength between two parallel conducting plates separated by 2.75 cm is 7.6 x104 V/m. What is the potential difference between the plates, in kilovolts? What is the potential difference, in volts, if the plates are only separated by 1.00 cm?

A proton is between the plates of a parallel plate capacitor. The charge density of the plates is 5 nC/m2. What is the acceleration of the proton?

Problem 13:   Each plate of a parallel-plate capacitor has an area of A = 0.61 m2. The plate separation is 3.0 mm, and one of these plates is shown in the figure. It carries a charge of Q = 2.9 μC, which is concentrated on its inner surface. Imagine a cylindrical Gaussian surface, of radius r = 0.012 m, whose axis is perpendicular to the plates. One end of the cylinder is inside the plate shown and the other end is located between the plates. Both ends are parallel to the plates. Part (a)  What is the flux through surface 1 Φ1, in newton meters squared per coulomb?  Part (b)  What is the flux through surface 2 (the outside of the cylinder not including the ends), in newton meters squared per coulomb?  Part (c)  What is the flux through surface 3 Φ3, in newton meters squared per coulomb?  Part (d)  Using all of your results, input an expression for the field within the capacitor E, in terms of the quantities given in the problem.

An insulating sphere of radius R = 3 cm has positive charge uniformly distributed throughout its entire volume. The electric field at the surface of the sphere has a magnitude of E = 5x107 V/m (a) [3 points] Calculate the volumetric charge density p of the sphere (in C/m3) and Calculate the magnitude of the electric field at a point located atr= 1cm, inside the insulator.

A parallel plate capacitor has metal plates, each of area 1.25 m2, separated by 1.80 mm. What charge (in µC) is stored in this capacitor if a voltage of 2.10 ✕ 103 V is applied to it?   µC

A spherical capacitor is composed of two concentric conducting spheres, one of radius a and the other of radius c (c > a). In addition, between the two conductors there is a spherical shell of dielectric material (relative permittivity/relative dielectric constant ) with inner radius b (c > b > a) and outer radius c. The charge on the inner conductor is +Q. The charge on the outer conductor is -Q. (a) Make a sketch of the situation, indicating the relevant dimensions. (b) Determine the magnitude of the electric field E at radius r for a < r < b. (c) Determine the magnitude of the electric field E at radius r for b < r < c. (d) What is the (induced) surface charge density on the inner surface of the dielectric. (e) Sketch the radial component of the electric field versus r . (f) Sketch the electrostatic potential versus r . (g)Calculate the potential difference between the conductor at r = a and that at r = c. (h) What is the capacitance of this capacitor?