Positive point charges are placed at three corners of a rectangle, as shown in the figure. (a) W

Positive point charges are placed at three corners of a...

Key Concepts

Electric Field from a Point Charge

This concept describes the region around a point charge in which the charge exerts an influence on other charges. The field is defined as the force per unit charge and is calculated using Coulomb's law, where the magnitude is proportional to the charge and inversely proportional to the square of the distance from the charge. This concept allows us to determine how much ‘push’ or ‘pull’ a charge will exert on another charge in its vicinity.

Principle of Superposition

The superposition principle is essential in electromagnetism because it states that the total electric field created at any point by a collection of charges is the vector sum of the individual electric fields created by each charge. This means that when multiple charges are present, their fields add together, both in magnitude and direction, to produce the net field. This principle simplifies the analysis of complex charge configurations by allowing us to consider each charge separately.

Electric Force on a Charged Particle

This concept relates to how a charged particle behaves when placed in an electric field. The force experienced by the particle is given by the product of its charge and the electric field (F = qE). It indicates that not only the magnitude of the electric field matters but also the sign of the charge, dictating the direction of the force. This fundamental relationship is central to understanding interactions between electric charges.

Vector Addition

Electric fields and forces are vector quantities, meaning they have both magnitude and direction. Vector addition is the process of combining these quantities to obtain a resultant vector. In electrostatic problems, considering the directional components of each individual electric field or force is crucial, as their contributions combine differently along various axes to form the net effect.

Transcript

00:01 So we're looking at three charges on three corners of a four -corner rectangle.

00:06 And we want to know what the electric field is at that fourth corner.

00:10 Well, electric field is a vector quantity, so there's going to be a direction involved, and that means it adds vectorially.

00:18 So we can just do the electric field for each individual charge and then add them up.

00:23 This is how we find the electric field.

00:26 We have our coolums constant.

00:28 We're going to call this 9 times 10 to the 9.

00:32 Then we have the distance between the charge and the point we're looking at.

00:39 And then we get rid of this line.

00:42 And then we have the charge in question.

00:44 We want this to be in kulams.

00:48 And this is going to be in meters down here.

00:51 This little r vector means that just the direction that it's pointing in, which is going to be fine for this four microculem, it's only going to be left or right.

01:01 And for this negative one microculem, it's only going to be up or down.

01:06 It's the 6 microculem one that's going to have an x and a y component because it's going to be going to be going diagonally.

01:15 So we're going to need to get the angle here so we can figure out those.

01:19 And that's going to be all right because we can use tan theta is the opposite side over the adjacent side.

01:29 Right? so that means our opposite side is the 0 .20 meters and our adjacent side is the 0 .50.

01:37 So we can say that inverse 10, 0 .2 over 0 .5, theta, and we'll get something around 21 .8 degrees.

01:49 That's going to help us out.

01:52 Okay.

01:57 Let's start with that one, because it's the more difficult ones.

02:00 So we'll break it into components, and then we can add those components to the other ones, right? so if we have 2 oomte constant of 9 times 10 to 9, and we have six microchulams, that's 10 to the minus 6.

02:23 We need to use good old pythagorean theorem to find this distance.

02:32 And you know, that's 0 .2 squared plus 0 .5 squared, all square rooted.

02:40 You'll get 0 .535 meters.

02:48 We can just round that to 0 .54 .0 .54 squared.

03:07 And we're going to use this angle that we got here.

03:10 This is 21 .8 degrees because if we want the x component, we're going to do cosine of 21 .8 degrees, x component.

03:30 And then for our y component, we're going to have sign of 21 .8 degrees.

03:38 You may use i hat and j hat.

03:43 I'm used to using x hat and y hat.

03:44 It just means in the x direction or in the y direction so you can just plug this in your calculator nine times uh 10 to the ninth power times six times 10 to the minus six power and it's divided by 0 .54 squared so out in front here we have 185 000 185 newtons and in the x direction we're going to multiply that by 0 .93 for the x direction and 0 .37 for the y direction make some space up here and we have from the plus six microculeum charge 68 ,772 newtons and then we have 172 ,22 newtons and then we have 172 ,22 newtons in that direction.

05:19 Okay, so that's our e field from the 6 quorum charge.

05:28 Let's go to one of the other ones and add those to it.

05:34 So let's start with the 4 microchulom charge...

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