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Find the energy of uniformly charged spherical shell of total charge Q and radius R.
3. Uniformly Charged Spherical Shell Find the energy of a uniformly charged spherical shell of total...
1.) Consider a spherical shell of radius R uniformly charged with a total charge of -Q. Starting at the surface of the shell going outwards, there is a uniform distribution of positive charge in a space such that the electric field at R+h vanishes, where R>>h. What is the positive charge density? Hint: We can use a binomial expansion approximation to find volume: (R + r)" = R" (1 + rR-')" ~R" (1 + nrR-1) or (R + r)" =R"...
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...
5. A thick, nonconducting spherical shell with a total charge of Q distributed uniformly has an inner radius R1 and an outer radius R2. Calculate the resulting electric field in the three regions r<RI, RL<r<R2, and r > R2
A uniformly charged non-conducting sphere of radius a is placed at the center of a spherical conducting shell of inner radius b and outer radius c. A charge +Q is distributed uniformly throughout the inner sphere. The outer shell has charge -Q. Using Gauss' Law: a) Determine the electric field in the region r< a b) Determine the electric field in the region a < r < b c) Determine the electric field in the region r > c d)...
Can someone prove those four equations for me? Applying Gauss's Law. Spherical Symmetrv: A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell's charge were concentrated at the center of the shell If a charged particle is located inside a shell of uniform charge, there is no electrostatic force on the particle from the shell. Enclosed charge is q Gaussian surface Si The dots represent a spherically symmetric distribution...
(ii) Use Gauss' law to show that the electric field outside a uniformly charged spherical shell (of positive charge Q) is equal to the electric field of a positive point charge Q placed at the center of the shell.
3. A uniformly charged sphere of radius 'a' has a charge density po. Find D everywhere using Gauss's law. Plot the magnitude of D vs R 4. A spherical shell of radius R 1 m has a surface charge density on it of пс and another spherical shell of radius R= 2m has a surface +8 Ps т? пс -6- т2 charge density of ps Find D at R= 3m
4. Using the formula V(r) 1 /TTda , calculate the potential inside and outside a uniformly charged spherical shell of total charge q and radius R A useful formula fo VR-2Rz cos& =[1 Virw-mcosor sine'de'
A thin spherical shell of radius R = 20.0 cm has total charge Q = 58.0 nC uniformly distributed on its surface. Part A A test particle with charge q = 8.00 nC is initially at a position r = 43.0 cm from the center of the shell. The particle moves to the surface of the shell closest to its initial position. What is the change in potential energy of the test particle as a result of this move? Part...
Find the energy of a uniformly charged solid sphere in the following way: Assemble it like a snowball, layer by layer, each time bringing in an infinitesimal charge dg from far away and smearing it uniformly over the surface, thereby increasing the radius How much work dW does it take to build up the radius by an amount dr? Integrate this to find the work necessary to create the entire sphere of radius R and total charge q.