find the magnitude of the electric field
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Q: a b - 3Q
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Q: just g and h, please.
A: Solution:
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A: uniform surface charge = 8pC/m2 h=889 m
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A thin disk with a circular hole at its center, called an annulus, has inner radius R1 and outer radius R2. The disk has a uniform positive surface charge density σ on its surface.
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- A solid disk of radius R = 11 cm lies in the y-z plane with the center at the origin. The disk carries a uniformly distributed total charge Q = 45 μC. A point P is located on the positive half of the x-axis a distance 24 cm from the origin. Refer to the diagram, where the y- and z-axes lie in the plane of the screen and the x-axis points out of the screen. a. Enter an expression for the surface charge density σ in terms of the total charge and radius of the disk. σ = b. Consider a thin ring of the disk of width dr located a distance r from the center. Enter an equation for the infinitesimal charge in this thin ring in terms of Q, R, r, and dr. dQ = c. Calculate the electric potential at P, in kilovolts. V = d. Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb. E =Consider two nested, spherical conducting shells shown in grey and red in the figure 7. The first has inner radius a and outer radius b. The second has inner radius c and outer radius d. Case I A positive charge +Q is introduced into the center of the inner spherical shell (the grey shell). Asnwer case IConsider a solid uniformly charged dielectric sphere where the charge density is give as ρ. The sphere has a radius R. Say that a hollow of charge has been created within the spherethat is offset from the center of the large sphere such that the small hollow has its center on the x axis where x = R/2. Using a standard frame where the large frame has its center at the origin, find the Electric field vector at the following points. a.The origin b.Anywhere inside the hollow (challenging) c.x = 0, y = R d.x = -R, y =0
- We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1bAn infinitely long rod lies along the x-axis and carries a uniform linear charge density λ = 5 μC/m. A hollow cone segment of height H = 27 cm lies concentric with the x-axis. The end around the origin has a radius R1 = 8 cm and the far end has a radius R2 = 16 cm. Refer to the figure. a. Consider the conic surface to be sliced vertically into an infinite number of rings, each of radius r and infinitesimal thickness dx. Enter an expression for the electric flux differential through one of these infinitesimal rings in terms of λ, x, and the Coulomb constant k. b. Integrate the electric flux over the length of the cone to find an expression for the total flux through the curved part of the cone (not including the top and bottom) in terms of λ, H, and the Coulomb constant k. Enter the expression you find. c. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = 0. d. Calculate the electric flux, in N•m2/C, through the circular end of the cone at x = H. e.…The Electric Field of a Charged Cylinder and a Concentric Cylindrical Shell. A non-conducting cylinder of radius a is charged with charge density p(r) = p.r, where r is the distance from the cylinder axis. The cylinder is placed inside a shell with cylindrical inner and outer radii b and c, respectively. The outer shell is charged with a uniform charge density p(r) = Po. The cylinder and the shell are concentric (see figure). D B b 0 Derive the formulas for the magnitude of the electric field at points A, B, C, and D. Guidance: 1. If required by the formulas, specify Coulomb's force constant through the Vacuum Permittivity, E = 1/4nk instead of Coulomb's onstant, k. 2. Type epso, rhoo, and pi, if the respective symbols Eo,Po, and n, are required.
- A ball of conductor of radius RE has total Charge 2Q and a concentric spherical cavity of radius R₁ > RE. At the exact center of the cavity is a charge 3Q. Find the charge q at the radius RE and supply the missing numerical factor below. q=1 Qsuppose I have a square of charge with a uniform charge density lying in the x-y plane with one corner at the origin and the other corner at (L,L,0). The total charge is Q. Determine the electric field at (0,0,Z).In the example of a uniform charged sphere p0 = Q/((4/3)πR3). Rewrite the electric field in terms of the total charge Q on the sphere. Do this for the range r > R. Do this for the range r < R.