The two charges q1 and q2 shown in Fig. E21.34 have equal...

The two charges $q_{1}$ and $q_{2}$ shown in Fig. E21.34 have equal magnitudes. What is the direction of the net electric field due to these two charges at points $A$ (midway between the charges), $B,$ and $C$ if (a) both charges are negative, (b) both charges are positive, (c) $q_{1}$ is positive and $q_{2}$ is negative.

Key Concepts

Electric Field from a Point Charge

This concept explains that a point charge produces an electric field that radiates outward if the charge is positive and inward if the charge is negative, with a magnitude that diminishes as the square of the distance from the charge, according to Coulomb’s law.

Superposition Principle

In electrostatics, the net electric field at any given point is the vector sum of the electric fields produced by each individual charge. This principle allows one to calculate the overall field even for complex arrangements by summing the contributions from all charges.

Effect of Charge Sign on Field Direction

The sign of a charge determines the direction of the electric field lines it produces: positive charges create fields that emanate outward, while negative charges produce fields that converge inward. This behavior is essential in predicting the direction of the net field in multi-charge systems.

Symmetry in Charge Configurations

When charges are arranged symmetrically, certain geometric relations can simplify the analysis of the electric field. Recognizing symmetry in a system helps identify regions where components of the fields cancel or reinforce one another, making it easier to determine the net field direction.

Transcript

00:01 Charges q and 1, and i've drawn these here, they have equal magnitudes.

00:10 And we want the, what is the direction of the net electric field due to these at point a, b, and c.

00:47 A, if both charges are negative.

00:59 So if both charges are negative.

01:01 Okay, let's go figure this out.

01:05 The electric field through the first charge, a, b, and c.

01:18 Okay, so the first charge will be e1 equals kq1 over r squared times minus i.

01:32 And e2 will be kq2 over r2i.

01:43 To account q1 equals q2.

01:51 We know that since q1 equals q2, we can say that e1 times k, e1, those will be the same, times i negative, e will equal this plus e2, i positive, that will equal 0.

02:35 Okay, so then we can continue with e will equal negative 2e times the sign of theta times j and that will equal negative 2 kq1 times y over r cubed.

02:58 We should recognize that times j.

03:04 Then and so that will give me e will equal to equal to e.

03:18 Times the sine of theta j times 2 k u1y over r cubed i get this right here and that'll be j as well so the charge on a will equal e and that'll be equal to zero and b will be equal to negative j and c will be equal to just j for my next order of business, my charges are going to be both positive.

04:09 Both charges are positive.

04:13 Okay, so we've got the same thing right here.

04:17 So let me go back here.

04:25 Hang on just a second.

04:33 So i forgot a step here...

Please give Ace some feedback