The plane z = 0 marks the boundary between free space (z < 0 side) and a dielectric medium (z > 0 side) with a relative permittivity of e, =35. The electric field intensity next to the interface in free space is Ē = -10£ + 25ŷ + 92 V/m. Determine the electric field intensity on the other side of the interface.
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- The electric field between two concentric cylindrical conductor at r = 0.01m and r = 0.05 m is given by E 105 f. The energy stored in a 0.5 length (assuming free space) 2.224 J O 1.224 J O 3.224 J O 0.224 JA 3.0 cm × 3.0 cm parallel-plate capacitor has a 1.0 mm spacing. The electric field strength inside the capacitor is 1.5×105 V/m .How much charge is on each plate?A dielectric rod with cross-section area of A and polarization of Px = ax² + b is extended from x = 0 to x = L. (a) Calculate the bound volume charge density and bound surface charge density. b) Determine the total bound charge.
- A capacitor is composed of two metal plates. The two plates have the dimensions L = 0.11 m and W = 0.56 m. The plates have a distance between them of d = 0.1 m, and are parallel to each other. Part (a) The plates are connected to a battery and charged such that the first plate has a charge of q. Write an expression for the magnitude of the electric field, |E|, halfway between the plates. Part (b) Input an expression for the magnitude of the electric field, |E2|, just in front of plate two. Part (c) If plate two has a total charge of q = -1 mC, what is its charge density, σ, in C/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.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.
- Please AsapA 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?