The inner sphere has a net charge of +6 μC and the shell has a net charge of -6 μC.

Name: Problem 61, Chapter 16: Physics
Uploaded: 2021-07-16T17:01:37-08:00
Duration: 5 min 2 s
Channel: Jose Carlos
Description: The inner sphere has a net charge of +6 μC and the shell has a net charge of -6 μC.

step 1 In part A of this problem, we have to draw field lines. And to do that, let's remember the two k

The inner sphere has a net charge of +6 μC and the shell has...

Key Concepts

Charge Distribution

Charge distribution concerns how electrical charge is spread over a material. It is important to distinguish between the net charge and the surface charge density on different parts of a system. In composite systems like an inner sphere and an outer shell, the individual net charges help determine the electric field configuration in each region.

Spherical Symmetry

Spherical symmetry implies that the physical properties of a system are the same in every direction from a central point. This symmetry simplifies the mathematical treatment of electric fields and potentials, as it allows the use of spherical Gaussian surfaces to derive analytic expressions.

Conductors in Electrostatic Equilibrium

In conductors, charges move freely and redistribute themselves until the internal electric field is zero. This results in any excess charge residing solely on the conductor's surface. Understanding this behavior is key when analyzing charge distributions on spherical conductors and shells.

Gauss’s Law

Gauss’s law relates the net electric flux through a closed surface to the charge enclosed by that surface. This principle is crucial when determining the electric field resulting from symmetric charge distributions, such as those on spheres, and is a cornerstone in solving many electrostatics problems.

Transcript

00:01 In part a of this problem, we have to draw field lines.

00:05 And to do that, let's remember the two key ideas that we need to have for drawing field lines.

00:12 The first one is that field lines point away from positive charges and towards negative charges.

00:19 The second one is that there can be no field lines inside conducting materials.

00:26 Taking these two principles into account, we know that the inner sphere has positive, 6 microculems and the outer sphere has negative 6 microcule.

00:41 So that means that our field lines have to start at the edge, the surface of the inner sphere and they go towards the negative.

00:55 They stop there because the shell is also made out of a conductic material.

01:05 Now field lines don't go beyond this point because let's remember that.

01:11 That gossus law states that the flux is equal to the charge enclosed over the permittivity free space.

01:28 But we have positive 6 and negative 6 microplomans.

01:31 So that charge and closed beyond the shell is zero.

01:37 So that is why we cannot have any fields outside the shell.

01:42 Now let's move on to part b.

01:44 And let's use a fresh diagram to work on that.

01:49 And let's remember that we have some net charge, some positive net charge over here.

01:57 These positive charges are attracting negative ones.

02:02 And while we know that we can find some negative charges outside as well...

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