The charge density function below describes a long cylindrical charge distribution -{(1. Po (1-r/R) for r ≤ R elsewhere Please determine the electric field everywhere due to this charge distribution. Explain your steps.
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- Consider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.Repeat your calculations for the preceding problem (shown below),given that the charge is distributed uniformly over thesurface of a spherical conductor of radius 10.0 cm. A charge of −30 μC is distributed uniformlythroughout a spherical volume of radius 10.0 cm.Determine the electric field due to this charge at a distanceof (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the centerof the sphere.A large non-conducting slab of area A and thickness d has a charge density rho=Cx^4. The origin is through the center of the slab. That is to say, it bisects the slab into two equal volumes of d/2 thickness and with an area of A, with -d/2 to the left of x=0, and d/2 to the right of x=0. Express all answers in terms of C, x, and any known constants. Gaussian surface 1 (cylinder) is located such that its volume encompasses the charge contained within the slab. Apply Gauss's Law to cylinder 1 to determine the electric field to the left and to the right of the slab. Make sure you incude the domains over which the field is valid.
- Consider two concentric insulating cylinders of infinite length. The inner cylinder is solid with radius R, while the outer cylinder is a hollow shell with inner radius a and outer radius b. Both cylinders have the same volume charge density of +ρ. Using Gauss’s Law, find the electric field as a function of r (where r= 0 at the central axis) in the interval a≤r < b. Note: Your final equation should be in terms of given parameters of ρ,a,b,R, and r.Hello, 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?Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2 , respectively. They are separated at center-to-center distance a (see below). Find the electric field at point P located at a distance r from the center of sphere 1 and is in the direction from the line joining the two spheres assuming their charge densities are not affected by the presence of the other sphere. (Hint: Work one sphere at a time and use the superposition principle.)
- A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and Q , respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) ra; (b) arb; and (c) rb.The figure here shows a Gaussian cube of face area Aimmersed in a uniform electric field that has the positivedirection of the z axis. In terms of E and A, what is the fluxthrough (a) the front face (which is in the xy plane), (b) therear face, (c) the top face, and (d) the whole cube?Charge is distributed uniformly with a density ρ throughout an infinitely long cylindrical volume ofradius R. Show that the field of this charge distribution is directed radially with respect to the cylinder.
- Determine the total charge distribution on r = b, and on r = a., explain Check if the electrical field for this configuration match the findings that for all points r inside the circle r<a is E= q/4piΕor2 and for all points r outside the shell r>a is E=0Find all the bound charges and the total charge of a dielectric sphere of radius a carrying polarization P = rr ̂ ?A “semi-infinite” non-conducting rod (that is, infinite in one direction only) has uniform linear chargedensity(lambda). Show that the electric field at point P makes an angle of 45⁰ with the rod and that this result isindependent of the distance R. To do this, separately find the parallel and perpendicular (to the rod) components of the electric fieldat P, and show that these components are equal