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)
What If? What if the charge density as a function of r within the charged solid sphere is given by ρ = a/r^2 ? Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ε0.)
magnitude E=
a)
ρ = volume charge density = a/r
small charge enclosed is given as
dq = ρ dV
dq = (a/r ) ( 4πr2dr )
dq = 4π a r dr
total charge is given as
Q = 4π a r dr
Q = 4π a r2/2
using gauss's law
E A = Q/
E (4π r2) = 4π a r2/(2)
E = a/(2)
B)
ρ = volume charge density = a/r2
small charge enclosed is given as
dq = ρ dV
dq = (a/r2 ) ( 4πr2dr )
dq = 4π a dr
total charge is given as
Q = 4π a dr
Q = 4π a r
using gauss's law
E A = Q/
E (4π r2) = 4π a r/(2)
E = a/(2r)
A solid sphere, made of an insulating material, has a volume charge density of ρ =...
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