The two charges q1 and q2 shown in Fig. E21.38 have equal magnitudes. What is the direction of t

step 1 Alright, so in this problem, so we have a setup like this. So we have Q1, Q2, and this is the ce

The two charges q1 and q2 shown in Fig. E21.38 have equal...

The two charges $q_1$ and $q_2$ shown in $\textbf{Fig. E21.38}$ 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

00:02 Alright, so in this problem, so we have a setup like this.

00:09 So we have q1, q2, and this is the center line between them.

00:18 So we have three interested points, a, which is here, b is here, and c is right here.

00:27 So for part a, if q1, q2, they're both positive.

00:32 So we want to determine the direction of the electric field.

00:35 Fields at the three points.

00:38 So if q1, q2 they are both positive.

00:42 So at point a, the electric field induced by q1 is to the right.

00:47 And by the way, yeah, q1, q2, they have the same magnitude.

00:53 And the electric field induced by q2 is pointed to the right.

00:56 So there is no any electric field at point a.

01:01 But at point b, the electric field induced by qa is point to this direction and induced by q2 is pointing to that direction and this two actually the x component is cancelled out so just based on the symmetry so the only left component is pointing out okay so this is the combined component and similarly for the point c it is pointing down okay just because this one this one the the x component they are cancelled out.

01:38 And for part b, if q1, q2, they are negative, i use the red color.

01:47 So at point a, apparently the electric field induced by q1 is pointing to the left, and electric field induced by q2 is pointing to right...

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