Two point charges lie along the y -axis. A charge of q1= -9.0 μC is at y=6.0 m, and a charge of

step 1 So a few things about the electric field of point charges. So it has a formula that we can work

Two point charges lie along the y -axis. A charge of q1=...

Key Concepts

Equilibrium Points in Electric Fields

An equilibrium point in an electric field occurs where the net electric field is zero. Finding such points involves setting the vector sum of the electric fields from all charges equal to zero and solving for the position. This concept is fundamental in understanding points of balance in the influence of charged objects, where a test charge would experience no net force.

Superposition Principle

The superposition principle states that the total electric field created by a group of charges is the vector sum of the individual fields produced by each charge separately. This principle is essential when dealing with multiple charges, as it enables one to analyze complex charge configurations by considering the contributions from each charge and summing them to find the net effect.

Coulomb's Law

Coulomb's Law describes the force between two point charges and forms the basis for calculating electric fields in electrostatics. It states that the magnitude of the electric force between two point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental to understanding how individual charges influence the space around them.

Electric Field Due to a Point Charge

The electric field due to a point charge is defined as the force per unit positive charge that would be exerted on a small test charge placed in the field. Its magnitude is given by the expression E = k|q|/r², where 'k' is Coulomb's constant, 'q' is the charge, and 'r' is the distance from the charge. This concept is crucial because it allows us to calculate how a single charge affects other charges in its vicinity.

Transcript

00:01 So a few things about the electric field of point charges.

00:06 So it has a formula that we can work out from kulam's law.

00:12 It is a vector.

00:14 The magnitude of the vector is k absolute value of charge over r squared.

00:24 So r is the distance from the point charge to the point of observation.

00:28 And then the direction is r -hat, which is along a line joining the point charge to the observation point along that line.

00:44 So here we're going to be using the equation for two different point charges.

00:54 And what we know is that the total electric field from any number of point charges comes just from adding their individual electric fields at a point.

01:09 The point of observation, of course, is where you imagine something placed.

01:14 There's nothing really there.

01:18 So in this case, what we'd like to do is find a point near these two point charges along the y .i.

01:27 Axis where the electric field is zero.

01:31 And we know that at that point, we'll have to be a little bit closer to q2 than the q1.

01:37 So i'll kind of show it a little bit over four meters away from q2 and a little bit over five meters from q1.

01:51 So somewhere in there.

01:52 That's our observation point.

01:54 And at that point, we know that e1 is pointing into q1, and we know that e2 is pointing into q2, and so there must be a place where those two balance.

02:11 And we have a more specific situation that the two magnitudes of those two electric fields cancel.

02:22 So we can simply set up that cancellation.

02:25 We have k times nine, microculems and the micro will cancel, but we'll go ahead and write it in there for now.

02:35 Over, let's give it a separation.

02:44 R1 is equal to 6 minus y.

02:51 Y is the coordinate of the observation point, and r2 then is going to be 4 plus y.

03:01 And we don't know what y is, that is what we are going to try to find.

03:09 So the two separations come in with a square.

03:16 Let's see, we have eight microculems on the other side with 4 plus y squared.

03:23 And like usual, this is going to lead to a quadratic equation that we have to solve.

03:30 The micro and some of the constant type stuff cancels...

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