a) By reflecting on the symmetry of the charge distribution of the system, determine what the E-field lines look like outside the sphere for any r> R. Describe the E-field in words and with a simple sketch. Make sure to also show the direction of the E-field lines. b) Consider a point P, shown in the figure below, at a distance rp from the center of the sphere. Your goal for this part is to properly use Gauss' law to caleulate the electric field at point P. Choose an appropriate Gaussian surface and clearly draw it on a sketch of the wire. Show your calculation for the electric flux through the Gaussian surface, as well as for the charge enclosed. What at is the electric field at point P? Give both the magnitude and direction (give the magnitude in terms of the given quantities: Q, R, rp).

a) By reflecting on the symmetry of the charge distribution of the system, determine what the E-field lines look like outside the sphere for any r> R. Describe the E-field in words and with a simple sketch. Make sure to also show the direction of the E-field lines. b) Consider a point P, shown in the figure below, at a distance rp from the center of the sphere. Your goal for this part is to properly use Gauss' law to caleulate the electric field at point P. Choose an appropriate Gaussian surface and clearly draw it on a sketch of the wire. Show your calculation for the electric flux through the Gaussian surface, as well as for the charge enclosed. What at is the electric field at point P? Give both the magnitude and direction (give the magnitude in terms of the given quantities: Q, R, rp).

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 86AP: Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2...

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

Problem 2: a conducting sphere
A conducting sphere has a positive net charge Q and radius R. (Note: since the sphere is conducting all
the charge is distributed on its surface.)
a) By reflecting on the symmetry of the charge distribution of the system, determine what the E-field
lines look like outside the sphere for any r > R. Describe the E-field in words and with a simple
sketch. Make sure to also show the direction of the E-field lines.
b) Consider a point P, shown in the figure below, at a distance rp from the center of the sphere. Your
goal for this part is to properly use Gauss' law to calculate the electric field at point P. Choose an
appropriate Gaussian surface and clearly draw it on a sketch of the wire. Show your calculation for
the electric flux through the Gaussian surface, as well as for the charge enclosed. What at is the
electric field at point P? Give both the magnitude and direction (give the magnitude in terms of the
given quantities: Q, R, rp).
c) Write an expression for the magnitude of the E field for any radius r > R.
d) Similarly to part b) use Gauss' law to determine the magnitude of the electric field for any radius r
inside the sphere, therefore for 0 <r < R.
e) Make a sketch of the magnitude of E(r) for any r > 0. Clearly show on your graph the behavior of
E(r) for both regions: 0 <r < R, and r > R.

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