3) Use Gauss’s Law a) Find the field inside and outside a sphere of radius ?,...
3) Use Gauss’s Law
a) Find the field inside and outside a sphere of radius ?, which carries a uniform volume charge density ?. Express your answer in terms of the total charge of the sphere, ?.
b) Draw a graph of |?| as a function of the distance from the center. There are (at least) two ways to do this problem, although you need to do it only one way.
c) Write a few sentences about a method that you did not use to solve this problem. Would the other method be easier or more difficult?
Homework Answers
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3) Use Gauss’s Law
a) Find the field inside and outside a sphere of radius ?,...
Find the field inside and outside a sphere of radius R, which carries a volume charge...
Find the field inside and outside a sphere of radius R, which carries a volume charge density purpo. Find Qenclosed for a Gaussian shape inside and outside the charge distribution. Find SE da for a Gaussian shape inside and outside the charge distribution.
(a) We have said that Gauss’s law is always true, but only useful for calculating the...
(a) We have said that Gauss’s law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss’s law to find the field of a sphere whose density depends on distance r from the center? Can we do it...
Consider a uniformly-charged sphere of radius 70 cm. The magnitude of the electric field outside of...
Consider a uniformly-charged sphere of radius 70 cm. The magnitude of the electric field outside of the sphere everywhere at a distance 10 cm from the sphere’s surface is 855 N/C, and points radially toward the center of the sphere. a) Use Gauss’s law to find the net charge within the sphere’s surface. Draw a figure showing the necessary information, and indicate your solution steps. b) Use Gauss’s law to find the electric field at a distance 35 cm from...
Gauss' Law Electric Field Inside a Cavity A sphere of radius 2m is made of a...
Gauss' Law Electric Field Inside a Cavity A sphere of radius 2m is made of a non-conducting material that has a uniform volume charge density p = 2.655 x 10-10C/m. A spherical cavity of radius 1m is then carved out from the sphere. As measured from the center of the large sphere, the center of the spherical cavity is at the position in cos300i+sin 30°i. Find the electric field at a point P within the cavity. As measured from the...
A non-uniformly charged sphere of radius R has a total charge Q. The electric field inside...
A non-uniformly charged sphere of radius R has a total charge Q. The electric field inside this charge distribution is described by E=Emax(r4 /R4 ), where Emax is a known constant. Using the differential form of Gauss’s law, find volume charge density as a function of r. Express your result in terms of r, R and Emax.
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=...
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...
Charge Q is uniformly distributed inside a sphere of radius R. (a) Determine the electric field...
Charge Q is uniformly distributed inside a sphere of radius R. (a) Determine the electric field inside and outside the sphere. Explain how you arrive at the answer. (b) A cavity of radius R/4, and centered at a point a distance R/2 from the center of the sphere, is made within the sphere. This means that within the sphere of radius R, there is a smaller sphere of radius R/4 which has no charge (the charge density is zero within...
Gauss’s law for electricity gave us a value for the electric field a distance r away...
Gauss’s law for electricity gave us a value for the electric field a distance r away (E = (1/4πε0)(qenclosed/r2). You have a conductive solid sphere (radius of a) inside a conductive shell (inner radius of b and outer radius of c). The sphere has a charge of +4Q while the shell has a charge of +10Q. Find the following: a. What is the electric field for r<a? What is the electric field for b>r>a? b. What is the net charge...
Find the field inside and outside a sphere of radius R, which carries a volume charge density purpo. Find Qenclosed for a Gaussian shape inside and outside the charge distribution. Find SE da for a Gaussian shape inside and outside the charge distribution.
Gauss' Law Electric Field Inside a Cavity A sphere of radius 2m is made of a non-conducting material that has a uniform volume charge density p = 2.655 x 10-10C/m. A spherical cavity of radius 1m is then carved out from the sphere. As measured from the center of the large sphere, the center of the spherical cavity is at the position in cos300i+sin 30°i. Find the electric field at a point P within the cavity. As measured from the...
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...
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