the figure below ghows four small spheres each with pogiive chargeatthe corners square the lengt

Step 1: Calculate the magnitude of the electric force on the sphere with charge Q.

The figure below ghows four small spheres each with pogiive...

The figure below shows four small spheres, each with a positive charge, at the corners of a square. The length of each side of the square is represented by s. The top-right sphere has a charge of Q; the lower-left sphere has a charge of -q; the other two spheres each have a charge of 2q. (Assume that the +x-axis is to the right and the +y-axis is along the page) What is the magnitude of the force on the sphere with charge Q? Express your answer in symbolic form. What is the direction of the force on the sphere with charge Q? Enter your answer in degrees counterclockwise from the +x-axis.

Transcript

0:00 All right, hello.

00:01 In this question, we're given this setup, where we have a square of charges, each separated by a distance a to make the square.

00:08 And the top left and bottom right charges have 5q.

00:11 Bottom left has 3 .5q.

00:13 And our top right charge, which is the one we're interested in, has a charge of just single q.

00:18 And we're asked, what is the net electric force on my charge in the top right, little q, so both magnitude and direction? in order to do this, let's go ahead and draw our forces on here.

00:33 So coming from the force below it, i'm going to have a force, electric force, going straight up.

00:40 And from the charge on the left, i'm going to have that same magnitude electric force going straight to the right.

00:46 And it's going to be the same magnitude, because this charge and this charge are the same distance away.

00:51 And they're the same magnitude of charge.

00:54 And so they're just pushing in opposite directions here, or in different directions, i should say.

00:58 So those will be both from the 5.

01:02 I'll keep those drawn in blue.

01:04 And then this 1 and 3 .5, well, it's a further distance away.

01:07 But it's going to be pushing directly away from it.

01:09 So this is going to be 45 degrees here.

01:12 And this is going to be the force electric from the, i'll call it, the 3, dropping the 0 .5 there.

01:19 So if i want to find the magnitude of my net field vector, well, i know that i'm going to have some x component and some y component.

01:30 And so if i want the magnitude, i'm going to have to take the square root of the sum of the squares there.

01:34 So let's go ahead and find fx.

01:37 Well, in this case, i have my force for my 5q charge going to the right.

01:43 And in the same direction, i have just the cosine component of my 3 .5 charge.

01:51 And so what are each of those charges going to be? well, i know an electric force is k times q1, which in this case will be this charge here, times q2, which for this 5 is going to be 5 .0q.

02:04 So that's q2.

02:06 Kq1q2 divided by r squared, where r is the distance.

02:10 So how far am i away from the 5 charge? well, i'm going to be just a distance of a.

02:15 And that's going to be squared...

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