Problem 3.35A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density po, and the "southern” hemisphere a uniform charge density -po. Find the approximate field E(r, 0) for points far from the sphere (r » R).
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![Problem 3.35 A solid sphere, radius R, is centered at the origin. The "northern”
hemisphere carries a uniform charge density po, and the "southern" hemisphere a
uniform charge density -po. Find the approximate field E(r, 0) for points far from
the sphere (r » R).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a11ce3d-21c0-472b-9212-b4fe5760ed67%2Fbd5f4aa0-0121-4a61-87ed-a974d8a22343%2Fyjl1vv_processed.png&w=3840&q=75)
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- A point charge Q is located on the axis of a disk of radius R at a distance b from the plane of the disk (Fig. Show that if one-fourth of the electric flux from the charge passes through the disk, then R = √3b. ). R Fig. bHello, I understand that to calculate the net charge in the shell, I need to integrate the equation from 4 cm to 6 cm with volume charge density times 2 * pi * r * dr. However, since the problem here provides me with a novel expression of p = b/r, I am a bit lost... Could you please tell me how I can solve such problem?There is a spherical thin shell of radius a. It carries uniform surface charge with a density of ps C/m2. (p = rho). Find the electric fields E at locations with distances R from the center of the spherical shell. Find E for points outside the spherical shell and inside the shell. Hello, I am getting tripped up for in my integration here. Could you help me with these concepts? Thank you.
- 1.27| The important dipole field (to be addressed in Chapter 4) is expressed in spherical coordinates as E =4 (2 cos 0 a, + sin 0 ag) where A is a constant, and where r> 0. See Figure 4.9 for a sketch. (a) Identify the surface on which the field is entirely perpendicular to the xy plane and express the field on that surface in cylindrical coordinates. (b) Identify the coordinate axis on which the field is entirely perpendicular to the xy plane and express the field there in cylindrical coordinates. (c) Specify the surface on which the field is entirely parallel to the xy plane.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.)A long non-conducting cylindrical wire of radius a stores a total charge Q₁ and is surrounded by a hollow, concentric conducting cylindrical shell or length L, inner radius b and outer radius c. The conducting cylindrical shell stores a total charge -30. See Figure. Using Gauss's law, write an equation for the electric field as a function of r (E(r)) inside the non-conducting cylinder (r< a). (When applying Gauss's Law, show derivation and the Gaussian surface, supporting your solution with geometrical reasoning.) Inner non-conducting b C + Outer conducting, solid cylinder of total charge -3Q
- An ∞ -planar slab of thickness 2d has constant charge density p, and p=0 for [y]>d. Find E everywhere. Find V everywhere (state your choice of reference). X 2 P .24answer for (d) and (e) pleaseConsider an infinitely long cylinder with radius R. The cylinder is an insulator and it is positively charged, the charge per unit of length is A. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume). By reflecting on the symmetry of the charge distribution of the system, determine what a) the E-field lines look like around the cylinder. Describe the E-field in words and with a simple sketch. In order to give a complete description of the E-field lines make two sketches: i) one with a side view of the cylinder, ii) one with a cross-sectional view of the cylinder. Make sure to also show the direction of the E-field lines. b) (-- . the figure. Your goal for this part is to properly use Gauss' law to calculate the electric field at point P. Follow the 5 steps below. Consider a point P outside the cylinder, at a distance d from its axis, d > R, as shown in
- An infinitely long cylindrical conductor of a radius r is charged with a uniformly distributed electrical charge, if the charge per unit length of it equal A coulomb/m. ( using gauss law) calculate the electric field at point d. d.Find the electric flux through a single side of regular octahedron of the side a 4cm with the charge 180 nC placed at the geometric centre of it. Take k to be 8.99x10° N/C. Give your answer to the nearest tenth of Nm2/C. Your Answer:A charge of 22.2 pC is distributed uniformly on a spherical surface (r1 = 2.0 cm), and a second charge of-9.2 pC is distributed uniformly on a concentric thin spherical surface (r2 = 4.0 cm). Determine the magnitude of the electric field ( in units of N/C) at a distance of 5.0 cm from the center of the two surfaces. Select one: O A. 3.90 O B. 46.80 OC. 32.50 OD. 59.80 OE. 113.04