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Problem 5. Consider a charged sphere with the following charge density 0 Using...
Consider a charged sphere with the following charge density ρ(r) =(ρ0(1− r Rmax) r ≤ Rmax...
Consider a charged sphere with the following charge density ρ(r)
=(ρ0(1− r Rmax) r ≤ Rmax 0 r > Rmax
Using Gauß’ law, calculate the electric field
(a) ~ E1 inside the sphere (i.e. r ≤ Rmax),
(b) ~ E2 outside the sphere (i.e r ≥ Rmax),
(c) Check that lim r→Rmax ~ E1 = lim r→Rmax ~ E2. Reminder: Due
to spherical symmetryRRRV ρ(r0)dxdydz =Rr 0 ρ(r0)4πr02dr0
Please provide an explanation for the
solution.
Problem 5. Consider a charged...
Problem 5. Consider a charged sphere with the following charge density r Rma Using Gauß' law,...
Problem 5. Consider a charged sphere with the following charge density r Rma Using Gauß' law, calculate the electric field Rma), (a) E1 inside the sphere (i.e. (b) E2 outside the sphere (i.e r 2 Rmaz), (c) Check that lim E,-lim É,. Reminder: Due to spherical symmetry JJfv ρ(r')dzdydz-Jo ρ(r')rrr2dr' max
Consider a sphere of radius a with a uniform charge distribution over its volume, and a...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows...
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 solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 ,...
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 , where A is a constant and r is measured from the center of the sphere. a) Show that the electric field outside the sphere (r > R) is E = AR5 /(5εor 2 ). b) Show that the electric field inside the sphere (r < R) is E = AR3 /(5εo). Hint: The total charge Q on the sphere is found by integrating ρ...
A spherical ball of radius R1 is charged with a constant charge density ρ. However a...
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...
(1) Consider a very long uniformly charged cylinder with volume charge density p and radius R...
(1) Consider a very long uniformly charged cylinder with volume charge density p and radius R (we can consider the cylinder as infinitely long). Use Gauss's law to find the electric field produced inside and outside the cylinder. Check that the electric field that you calculate inside and outside the cylinder takes the same value at a distance R from the symmetry axis of the cylinder (on the surface of the cylinder) .
Charge is distributed throughout a spherical volume of radius R with a density ρ ar where...
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,...
A uniformly charged non-conducting sphere of radius a is placed at the center of a spherical...
A uniformly charged non-conducting sphere of radius a is placed at the center of a spherical conducting shell of inner radius b and outer radius c. A charge +Q is distributed uniformly throughout the inner sphere. The outer shell has charge -Q. Using Gauss' Law: a) Determine the electric field in the region r< a b) Determine the electric field in the region a < r < b c) Determine the electric field in the region r > c d)...
A solid sphere, made of an insulating material, has a volume charge density of ρ =...
A solid sphere, made of an insulating material, has a volume charge density of ρ = a/r What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0.), where r is the radius from the center of the sphere, a is constant, and a > 0. magnitude E= (b)...
Consider a charged sphere with the following charge density ρ(r)
=(ρ0(1− r Rmax) r ≤ Rmax 0 r > Rmax
Using Gauß’ law, calculate the electric field
(a) ~ E1 inside the sphere (i.e. r ≤ Rmax),
(b) ~ E2 outside the sphere (i.e r ≥ Rmax),
(c) Check that lim r→Rmax ~ E1 = lim r→Rmax ~ E2. Reminder: Due
to spherical symmetryRRRV ρ(r0)dxdydz =Rr 0 ρ(r0)4πr02dr0
Please provide an explanation for the
solution.
Problem 5. Consider a charged...
Problem 5. Consider a charged sphere with the following charge density r Rma Using Gauß' law, calculate the electric field Rma), (a) E1 inside the sphere (i.e. (b) E2 outside the sphere (i.e r 2 Rmaz), (c) Check that lim E,-lim É,. Reminder: Due to spherical symmetry JJfv ρ(r')dzdydz-Jo ρ(r')rrr2dr' max
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
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,...
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