Consider a spherical Gaussian surface and three charges: q1=2.03 μC, q2=-3.28 μC, and q3=4.89 μC

Consider a spherical Gaussian surface and three charges:...

Consider a spherical Gaussian surface and three charges: $q_{1}=2.03 \mu C, q_{2}=-3.28 \mu C,$ and $q_{3}=4.89 \mu C .$ Find the electric flux through the Gaussian surface if it completely encloses (a) only charges $q_{1}$ and $q_{2},$ (b) only charges $q_{2}$ and $q_{3},$ and (c) all three charges. (d) Suppose a fourth charge, $Q$ is added to the situation described in part (c). Find the sign and magnitude of Qrequired to give zero electric flux through the surface.

Consider a spherical Gaussian surface and three charges:
$q_{1}=2.03 \mu C, q_{2}=-3.28 \mu C,$ and $q_{3}=4.89 \mu C .$ Find the electric
flux through the Gaussian surface if it completely encloses (a) only
charges $q_{1}$ and $q_{2},$ (b) only charges $q_{2}$ and $q_{3},$ and (c) all three
charges. (d) Suppose a fourth charge, $Q$ is added to the situation
described in part (c). Find the sign and magnitude of Qrequired to
give zero electric flux through the surface.

Key Concepts

Gauss's Law

Gauss's Law is a fundamental relation in electromagnetism which states that the net electric flux through any closed surface is equal to the net charge enclosed divided by the permittivity of free space. This law allows one to calculate electric fields for symmetric charge distributions by relating the electric flux to the enclosed charge, independent of the detailed shape of the field lines.

Electric Flux

Electric flux is a measure of the number of electric field lines passing through a given surface. It quantifies the field's effect over an area and is often used in Gauss's Law to connect the electric field with the source charges. The flux increases with both the strength of the field and the size of the surface through which the field lines pass.

Gaussian Surface

A Gaussian surface is an imaginary closed surface used to apply Gauss's Law. It is chosen to take advantage of symmetry in the charge distribution so that the electric field either has a constant magnitude or is perpendicular or parallel to the surface. This simplification makes it easier to calculate the total electric flux and, consequently, the electric field.

Net Enclosed Charge

The net enclosed charge is the algebraic sum of all the charges within a specified closed surface. In applying Gauss's Law, only this net charge contributes to the total electric flux through the surface. By understanding how individual charges interact—their signs and magnitudes—one can determine how the combined effect results in the observed electric flux, including cases where charges cancel each other out.

Transcript

00:01 Question 65.

00:02 It says to consider a spherical galsene surface and three charges presented here.

00:09 Find the electric flux through the galsine surface if it completely encloses the pairs of charges.

00:15 Q1 and q2, q2, q2 and q3, all three charges, and supports a fourth charge capital of q.

00:21 We'll get the part to in a second, but we'll just go part by part here.

00:25 So for the first part, we're saying we have a galsine surface that encloses q1 and q2.

00:31 So we know the flux through any given surface, galsing the surface i should say, is given by the relationship of enclosed charged q over epsilon not.

00:45 So for part a, this would mean that our charges enclosed are q1 plus q2 equals up.

00:51 So over epsilon not represent our total flux.

00:58 And so by plugging our values, i'll do yeah, 2 .03 minus 3 .28.

01:10 Micro coolomes so it's times 10 to negative 6 coulomes divided by our constant term epsilon not which is of course i'll write it out here because i won't write it out every time 8 .85 times 10 to negative 12 of the units of newton meters squared oh sorry reverse units of a flux so it's coulooms squared over newton meters there we go so evaluating this for our part a we would find that the flux then includes these first two charges to two to three similar figures is 1 .41 times 10 to the 5, i'm sorry, columns here, times 10 to the negative 5, that's not positive 5, that's right, 10 to the 5, newton meter squared or coulome.

02:06 So that's our solution for part a, part b, states that the two chargers that are in the gaussian surface now are q2 and q3.

02:17 So that means by the same logic of part a here, we have the same equation.

02:23 Just now it's q2 plus q3 over epsilon not...

Please give Ace some feedback