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In Fig-1, there are two infinite planes A and B, parallel to the YZ plane. Their surface charge densities are σA = −47nC/m2 and σB = 28nC/m2. The separation between the planes A and B is d = 10m.
a) Find the net electric field in unit vector notation in the region I, II, and III shown in Fig-1.
b) Now, we place a conducting spherical shell of radius R=0.1d in between the planes. The spherical shell conductor carries a surface charge density σ = −25μC/m2. The coordinates of the center(d/2,d/2,0), P1 (4d/5, d/2, 0) and P2 (d/2, d/4, 0). Find the net electric field at points P1 and P2 in unit vector notation.
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- Find the electric field a distance z from the center of a spherical surface of radius R (See attatched figure) that carries a uniform charge density σ . Treat the case z < R (inside) as well as z > R (outside). Express your answers in terms of the total charge q on the sphere. (Hint: Use the law of cosines to write r (script) in terms of R and θ . Be sure to take the positive square root: √(R2+z2−2Rz) = (R−z) if R > z, but it’s (z − R) if R < z.)Problem 2 Consider the Gaussian surface shown in Figure 2. A uniform external electric field E, having magnitude 3.20 x 103 N/C and parallel to the xz plane with an angle of 36.87° measured from the +x axis toward the +z axis, enters through face 1 (back face). In addition, a uniform electric field E, of magnitude 6.40 x 103 N/C traveling in the same direction as E, , flows outwardly through face 2 (front face). 0,45 m 0,30 m En 0.50 m Figure 2. Gaussian surface in the form of a prism through which two fields pass.Calculate the electric field at height h above the center of a square plate of size 2a×2a with uniform surface charge density η (both direction and magnitude). Verify that in the limit of large a the result agrees with the field of an infinite uniformly charged plane.
- Part 1 In Fig-1, there are two infinite planes A and B, parallel to YZ plane. Their surface charge densities are σA=34nC/m2 and σB=29nC/m2. The separation between the planes A and B is d=8m. Calculate the net electric field due to both the planes in unit vector notation in three regions shown in the Fig-1. a) (i) Find the electric field in unit vector notation in region I. x component of the electric field Give your answer to at least three significance digits.y component of the electric field Give your answer to at least three significance digits. (ii) Find the electric field in unit vector notation in region II. x component of the electric field Give your answer to at least three significance digits.y component of the electric field Give your answer to at least three significance digits. (iii) Find the electric field in unit vector notation in region III. x component of the electric field Give your answer to at least three significance digits. y component of the electric field Give…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 4.4.1bAs seen in Figure-3, there are loads with a volumetric charge density of pa=(3P)C/m^3 in the region with pε(0,a) of the coaxial cylinders nested in empty space.Radius p ε (b,c) in the region with a volumetric charge density pbc=(5/p^4)C/m^3, the cylinder surface with radius p=d It is very thin and on this surface σd=2C/m^2 density superficial charge. What is the electric field in each divided region? (a=2mm, b=4mm, c=6mm, d=8mm)
- Two conductors with concentric radii r1=13 m and r2=26 m are placed in such a way that their center is at the origin. While there is a charge Q1=7 µC on the cirdle with radius r1 and charge Q2=5 µC on the cirde with radius r2. Accordingly, find the amplitude of the electric field at point A(6, 7, 2). TT=3,1416 1 10-9 E= 36n Q2 r2 Q1 A X Yanıt: Seçiniz. *A thin rod has uniform charge per length z. The distance between point A and point B is 5W and the distance betweer point A and point C is 8W and the distance between point Cand point P is 2W. We introduce an integration variable h with h = 0 chosen to be at point B and the th direction to the left. The small r segment has length dh and charge dq. We want to find the electric field at point P. Draw it out--label the all the lengths and the integration variable! A B C PA 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 Q
- Problem 3: UP 6.53 Charge is distributed uniformly with a density p throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E(s) = ps 2€0 PR² 2€ S S≤R SZRPlease don't provide handwritten solution ......Ggg