4. A spherical region of space of radius 0.1 m has a volumetric charge density ρυ-kr2...
1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density. Let's make Pl =...
Charge is distributed throughout a spherical volume of radius R with a density ρ ar where α is a constant. an risthe distance from the center of the sphere. Determine the electric field due to the charge at a point a distance r from the center that is inside the sphere, and at a point a distance r from the center that is outside the sphere. (Enter the radial component of the electric field. Use the following as necessary: R,...
Exercise 22.19 A hollow, conducting sphere with an outer radius of 0.240 m and an inner radius of 0.200 m has a uniform surface charge density of +6.37 x 10-6 C/m². A charge of -0.500 μC is now introduced into the cavity inside the sphere. Part A What is the new charge density on the outside of the sphere?Part B Calculate the strength of the electric field just outside the sphere. Part CWhat is the electric flux through a spherical surface just inside the inner...
PROBLEM 2: A thick, spherical, insulating shell has an inner radius a and an outer radius b. The region a< r < b has a volume charge density given by p = A/r where A is a positive constant. At the center of the shell is a point charge of electric charge +q Determine the value of A such that the electric field magnitude, in the region a < r < b, is constant.
A positive point charge Q is located in free-space at the center of a spherical conducting shell The conducting shell consists of two concentric spheres, with inner radius a and an outer radius b (b> a), shaded region as shown in figure below. a) (15 points) Determine electric flux density everywhere. b) (5 points) Determine electric potential at the inner radius of the conducting shell c) (5 points) What is the total charge at the inner surface at r=a? justify...
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A point charge Q [C] is located at a point in space. The charge is surrounded by two spherical layers of materials as shown below. Both-materials have permitivity's different than free space (82 > ε), as indicated: (a) Calculate the electric flux density and field intensity everywhere in space. (b) Calculate the potential everywhere in space. (c) Plot the electric field intensity and electric flux density everywhere in space. (d) Calculate the energy stored...
A spherical ball of radius R1 is charged with a constant charge density ρ. However a smaller spherical hollow region of radius R2 is located at the center. Show that the electric field E inside the hollow region is uniform and find the electric field. When the electric field at any point in the cavity is equal to the electric field produced by the big sphere with uniform charge density ρ plus the electric field produced by the cavity with...
A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb. There is charge +q on the inner sphere and charge −q on the outer spherical shell. Take V to be zero when r is infinite. Part H Suppose the charge on the outer sphere is not -q but a negative charge of different magnitude, say -Q. Find the electric field at any point between the spheres ( ra...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center, p(r)=(C/r2)e-kr where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q. a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q. b) Show that C=...
A spherical metal (conductor) has a spherical cavity in side. There is a single point charge Q at the cavity center. The total charge on the meta is 0 (a) Describe how the charge is distributed on the E=? sphere. Would the surface charge density be u form at each surface? (b) Draw the electric field lines. c) Find the electric field for a point outside the metal. Express it in terms of r, the distance of the point in...