The inner sphere has a net charge of -6 μC and the shell has a net charge of +2 μC.

Name: Problem 62, Chapter 16: Physics
Uploaded: 2021-07-16T17:44:23-08:00
Duration: 6 min 17 s
Channel: Jose Carlos
Description: The inner sphere has a net charge of -6 μC and the shell has a net charge of +2 μC.

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

Key Concepts

Electrostatic Induction

Electrostatic induction refers to the process by which a charged object nearby a conductor causes the redistribution of charges within the conductor. Even without direct contact, the presence of an external charge can cause opposite charges to accumulate on the surface facing the external charge, influencing the overall charge distribution.

Electrostatic Shielding

Electrostatic shielding is the effect observed when a conductor rearranges its charges in response to external electric fields, effectively canceling these fields within its interior. This means that the interior of a closed conductor remains unaffected by external static electric fields, a concept essential for understanding fields in nested conductor systems.

Charge Distribution in Conductors

In conductors at electrostatic equilibrium, any excess charge resides on the surface. This is because charges move until they reach a configuration where the internal electric field is zero, which, in symmetric configurations such as spheres or shells, results in a uniform or easily determined surface distribution.

Gauss's Law

Gauss's law states that the total electric flux through a closed surface is proportional to the total charge enclosed within that surface. This principle is invaluable in problems with high symmetry, such as those involving spherical geometries, to calculate electric fields and understand how charges are distributed.

Transcript

00:01 In this problem, we need to draw the field lines for this arrangement of charges.

00:07 So let's go from the center to the outermost part drawing them.

00:12 First, we have the conducting sphere of charge, and we know that conductors cannot contain field lines inside of them.

00:20 So the field lines need to go from the edge of the sphere to the edge of the shell, because the shell is also made out of a conducting material.

00:29 So we have those field lines.

00:35 Now what about the direction? another principle we need to keep in mind is that field lines go from positive charges to negative charges.

00:46 So these charges, these field lines need to point inwards.

00:56 Great.

00:57 Now we are here and we know that there are no field lines inside of the shell, but what about outwards? well, we have the two microculems.

01:08 And negative 6 microculum.

01:11 So if we add these 2 up, we get negative 4 microculum.

01:15 So we still have some net charge outwards.

01:19 But it is not as strong as it is inwards, because we have these two positive charges blocking those negative 2 microculums.

01:32 So let's draw the field lines, but let's remember to draw less field lines to represent that decrease in the electric field.

01:42 So we'll just have four field lines, assuming that, let's say, these two get blocked by the outer shell.

01:54 Great, here we have our diagram.

01:57 Now let's talk about part b.

02:03 To find the charges on the outer and inner parts of the shell, we need to think about what is happening at the center.

02:12 We said that we have negative 6 microculems and that the electric field inside the shell is 0.

02:23 That tells us that we need to have positive 6 microculems in the inner portion because those have to cancel out this negative 6.

02:36 So this is for part b, for the radius b.

02:43 But we know that we have positive 6 microculems and we cannot simply create charges.

02:53 So what is happening is that in the outer portion, we are going to have negative 4 micropolems, which are going to cancel out 4 over here...

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