Problem #2 a) On a given surface S that bounds a volume T, the electrostatic potential...
Problem #2
a) On a given surface S that bounds a volume T, the electrostatic potential takes the constant value V0. The total charge inside the volume T is Q and there is no charge anywhere else. Show that the electrostatic energy contained in the space outside of S is :
?_E=(??_0)/2
b) Using the potential formalism (U_E = ∫∫∫ ? ??), find the energy required to assemble a solid sphere of radius R and charge Q.
Problem #3 : The bottom half of a shell of radius R carries a charge density ?(?) = ? cos(?) . Find the potential difference between the center and the “South pole” of the shell.
c) Do the same using the energy stored in the electric field.
Homework Answers
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Problem #2
a) On a given surface S that bounds a volume T, the
electrostatic potential...
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3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge density ρυ is cut in half as shown in the following...
(10%) Problem 8: A spherical capacitor consists of a single conducting sphere of radius R =...
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insulating sphere of radius a carries a positive charge 3Q, uniformly distributed its volume. Concentric with...
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1. Find the energy stored in a uniformly charged solid sphere of radius R with volume...
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Please help. Thank you.
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a) Find the total electrostatic energy stored in a uniformly charged sphere (not a shell) of radius R and charge q. Express your answer in terms of q, R, and constants of nature. There are many different ways to do this, we want you to use both of the following two different methods to check yourself. (i) Figure out E(r) and then use Griffiths Eq. 2.45 shown below (Be careful to integrate over all space, not just where the charge...
Problem 2. A solid metal sphere of radius R\ carries a charge -Q1, where Q1 >...
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Given a hollow spherical conducting shell (in electrostatic equilibrium) has an inner radius R1 and an...
Given a hollow spherical conducting shell (in electrostatic equilibrium) has an inner radius R1 and an outer radius R2 with a total charge -2Q distributed uniformly on its surfaces The inside of the hollow spherical conducting shell is filled with nonconducting gel with a total charge of -3Q distributed as p -p.*r (where po is a constant) through out the volume. -20 -5Qfadial for R2 4περη2 -3Q R1rR2 -3Qr2f ΑπερR14 adial 0<IR1 Assume V 0 @r0o 15. Find the absolute...
3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge density ρυ is cut in half as shown in the following figure. Find the force that the southern hemisphere exerts on the northern hemisphere and express it in terms of the total charge of the sphere q.
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insulating sphere of radius a carries a positive charge 3Q, uniformly distributed its volume. Concentric with this sphere a conducting spherical shell with inner radius b and outer radius c, and having a net charge -Q as shown in Figure. Find the charge distribution on the shell (charge on the inner radius b and charge on the outer radius c) when entire system is in electrostatic equilibrium.
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Please help. Thank you.
(3.) (40 pts) An insulating sphere of radius a has an embedded nonuniform charge den- sity: p(P) = (1+) where pe is a positive constant (this charge density is only valid for r <a). Sur- rounding the sphere, and concentric with it, is a conducting shell of inner radius b> a and outer radius c which is charged (not neutral). I do not know what the charge on the conductor is, but I am told that...
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