a (a) A solid sphere, made of an insulating material, has a volume charge density of p. where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius ? Note: The volume element dV for a spherical shell of radius rand thickness dr is equal to 4x2dr. (Use the following as necessary: a, r, and (g) magnitude E= direction magnitude E= a %0 p (b) What If? What if the charge density as a function of r within the charged solid sphere is given by F electric field within the sphere at radius r. (Use the following as necessary: a, r, and g-) 04 direction x Use a gaussian surface concentric with the sphere. How much charge is enclosed by the surface? Can you integrate over the spherical volume, using the given distribution and volume element, to find the charge? How does Gauss's law relate this charge to the flux? Using spherical symmetry, how can you relate the flux to the electric field and the area of the sphere? radially outward ? Find the new magnitude and direction of the x Use the same approach as in part (a). Integrating over the spherical volume, using the new expression for and the volume element, what is the new enclosed charge? Can you apply Gauss's law to this charge distribution, as in part (a), to find the field? radialy outward
a (a) A solid sphere, made of an insulating material, has a volume charge density of p. where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius ? Note: The volume element dV for a spherical shell of radius rand thickness dr is equal to 4x2dr. (Use the following as necessary: a, r, and (g) magnitude E= direction magnitude E= a %0 p (b) What If? What if the charge density as a function of r within the charged solid sphere is given by F electric field within the sphere at radius r. (Use the following as necessary: a, r, and g-) 04 direction x Use a gaussian surface concentric with the sphere. How much charge is enclosed by the surface? Can you integrate over the spherical volume, using the given distribution and volume element, to find the charge? How does Gauss's law relate this charge to the flux? Using spherical symmetry, how can you relate the flux to the electric field and the area of the sphere? radially outward ? Find the new magnitude and direction of the x Use the same approach as in part (a). Integrating over the spherical volume, using the new expression for and the volume element, what is the new enclosed charge? Can you apply Gauss's law to this charge distribution, as in part (a), to find the field? radialy outward
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11th Edition
ISBN:9781305952300
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:(a) A solid sphere, made of an insulating material, has a volume charge density of p where r is the radius from the center of the sphere, a is constant,
and a > 0. 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 4xr2dr. (Use the following as necessary: a, r, and g.)
magnitude
direction
E =
direction
a
%0
magnitude E =
a
Use a gaussian surface concentric with the sphere. How much charge is enclosed by the surface? Can you integrate over the spherical
volume, using the given distribution and volume element, to find the charge? How does Gauss's law relate this charge to the flux? Using
spherical symmetry, how can you relate the flux to the electric field and the area of the sphere?
radially outward
(b) What If? What if the charge density as a function of r within the charged solid sphere is given by p
electric field within the sphere at radius r. (Use the following as necessary: a, r, and co-)
Ega
r
-R
Find the new magnitude and direction of the
x
Use the same approach as in part (a). Integrating over the spherical volume, using the new expression for and the volume element,
what is the new enclosed charge? Can you apply Gauss's law to this charge distribution, as in part (a), to find the field?
radialy outward
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