Solve problem 6 How much work is required to assemble a uniform ball of charge with total (final) chargeQ and radius R? Hint: This is the same as the potential energy of the sphere, so useđU = V dq and imagine "building" the sphere a layer of thickness dr at a time. Alternatively,compute the work directly by bringing a charge dq in from infinity against the electric fieldof the charge already there (and distributed as a sphere of radius r).Problem 6.Compute the potential difference AV between: a) Two conducting spherical shells of radiusa and b with a charge +Q on the inner one and charge -Q on the outer one. b) Two(infinitely long) conducting cylindrical shells of radius a and b with a charge per unit length+A on the inner one and charge per unit length -A on the outer one. c) Two (infinite)conducting sheets of charge, one with charge +o on the ry plane and with with chargeparallel to the first one but at z =to understand Capacitance!d. Great! Now you've done almost all the work requiredProblem 7.Three thin conducting spherical shells have radii a < 6 < e respectively. Initially the shellwith radius a has a charge +Q and the shell with radius 6 has a charge -Q. You connectthe shells with radii a and e using a thin wire that passes through a tiny (insulated!) holethrough the middle shell and wnit for the chargo to como toThr m What in a)

Compute the potential difference between : Two conducting spherical shells of radius a and b with…

Answered: Compute the potential difference AV…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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Solve problem 6

How much work is required to assemble a uniform ball of charge with total (final) charge
Q and radius R? Hint: This is the same as the potential energy of the sphere, so use
đU = V dq and imagine "building" the sphere a layer of thickness dr at a time. Alternatively,
compute the work directly by bringing a charge dq in from infinity against the electric field
of the charge already there (and distributed as a sphere of radius r).
Problem 6.
Compute the potential difference AV between: a) Two conducting spherical shells of radius
a and b with a charge +Q on the inner one and charge -Q on the outer one. b) Two
(infinitely long) conducting cylindrical shells of radius a and b with a charge per unit length
+A on the inner one and charge per unit length -A on the outer one. c) Two (infinite)
conducting sheets of charge, one with charge +o on the ry plane and with with charge
parallel to the first one but at z =
to understand Capacitance!
d. Great! Now you've done almost all the work required
Problem 7.
Three thin conducting spherical shells have radii a < 6 < e respectively. Initially the shell
with radius a has a charge +Q and the shell with radius 6 has a charge -Q. You connect
the shells with radii a and e using a thin wire that passes through a tiny (insulated!) hole
through the middle shell and wnit for the chargo to como to
Thr m What in a)

Expert Solution

Step 1

Compute the potential difference between :

Two conducting spherical shells of radius a and b with charge +Q (inner) and -Q (outer).
Two conducting cylindrical shells of radius a and b with a charge per unit length + $λ$ (inner) and $- λ$ (outer).
Two conducting sheets of charge, one with charge $+ σ$ on the x-y plane and with charge $- σ$ parallel to the first one, at z = d.

Concepts & Formulas :

Gauss's theorem states that "the total electric flux out of a closed surface is proportional to the electric charge enclosed by the surface".

$φ = \oint \overset{⇀}{E} . d \overset{⇀}{s} = \frac{Q_{e n c l o s e d}}{ε_{o}}$

Potential difference, $∆ V = - \int \overset{⇀}{E} . d \overset{⇀}{l}$

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