April 1, 2015

Homework Help: Physics-Gauss' Law, hard

Posted by Bobby on Sunday, March 23, 2008 at 6:29pm.

Thank you Damon for answering my first questions fast and accurately. Do you or anybody else know how to do these harder Gauss' Law Problems?

1. A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q.
a) Describe the electric field lines both inside and outside the spheres (as if you had to draw field lines on the chart-no calculations).
b) Use Gauss' law to find an expression for the magnitude of the electric field between the spheres at a distance r from the center of the inner sphere (R<r<3R)
c) Calculate the potential difference between the two spheres.
d) The spheres are then connected by a conducting wire for long enough that the charges can redistribute. What is the final distribution charge on the two spheres?
e) The wire connecting the spheres is removed and the outside sphere is grounded. What is the charge distribution on the two spheres?

2. A long, insulating cylinder has a uniform charge density, ro=-2*mu*C/m^3, and a radius, R=15cm.
a) What is the total charge on a 40cm length of that cylinder?
b) Use Gauss' Law to find the electric field both inside and outside of the cylinder as a function of the distance from the center of the cylinder, r.
c) Set up an integral to evaluate the potential at the surface of hte cylinder (dont solve).
An isolated (ungrounded) conducting shell of inside radius 30cm and outside radius 40cm is now snapped together around the insulating cylinder.
d) What is the effect (qualitative) on the electric field at r=50cm?
e) What is the effect (qualitative) on the potential at the surface of the insulator.

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