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5. A sphere of radius R contains a uniform charge density p and is centered at...
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p.
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p. A spherical cavity of radius b is removed from sphere which is a distance z from the center of the sphere. Assume that a > z + b. a) Find the magnitude and direction of the electric field at point y0 which is separated by distance yo from the center of the sphere. b) Find the magnitude and direction of the electric field...
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 hollow sphere of radius a has uniform surface charge density σ and is centered at...
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
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...
P5. A sphere of radius 2a has a uniform volume charge density p. A spherical cavity...
P5. A sphere of radius 2a has a uniform volume charge density p. A spherical cavity of radius a is now removed from the sphere as shown. Show that the electric field within the cavity is uniform, has magnitude E-ρα/3e0, and is parallel to the common diameter of both spheres
4) A nonconducting sphere of radius Ro and total charge Q, contains a non-uniform volume charge...
4) A nonconducting sphere of radius Ro and total charge Q, contains a non-uniform volume charge density p -A/r (where A is a constant) throughout the she (a) Find the constant A in terms of Ro, k and Q (b) Find the electric field for r < Ro and r Ro.
A charged sphere of radius R (see picture below) has non-uniform volume charge density that is...
A charged sphere of radius R (see picture below) has non-uniform volume charge density that is proportional to distance its center O: rho(r) = br where b is a positive constant of proper units. (Consider values of R and b to be known) What are the proper units for constant b? b) Find electric potential V_0 at the center O.
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density...
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
P5. A sphere of radius 2a has a uniform volume charge density p. A spherical cavity of radius a is now removed from the sphere as shown. Show that the electric field within the cavity is uniform, has magnitude E-ρα/3e0, and is parallel to the common diameter of both spheres
4) A nonconducting sphere of radius Ro and total charge Q, contains a non-uniform volume charge density p -A/r (where A is a constant) throughout the she (a) Find the constant A in terms of Ro, k and Q (b) Find the electric field for r < Ro and r Ro.
A charged sphere of radius R (see picture below) has non-uniform volume charge density that is proportional to distance its center O: rho(r) = br where b is a positive constant of proper units. (Consider values of R and b to be known) What are the proper units for constant b? b) Find electric potential V_0 at the center O.
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
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