Where would you place a third small object with the same charge so that the electric field is ze

Where would you place a third small object with the same...

Key Concepts

Electric Field

This concept describes the region of space around a charged object where its force can be felt by other charges. It is a vector field, meaning it has both magnitude and direction, and it is the foundation for analyzing interactions between charges in electrostatics.

Coulomb's Law

Coulomb's Law provides the quantitative measure of the electric force between two point charges. It states that the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, which is essential for determining how the field strength varies with position.

Superposition Principle

The superposition principle asserts that the total electric field created by multiple charges is the vector sum of the individual fields produced by each charge. This principle is key to solving problems involving multiple charge configurations, as it allows one to determine where the fields cancel each other out.

Symmetry Considerations

Symmetry considerations help simplify the analysis of electric field problems by identifying points or lines where the effects of different charges cancel out. Recognizing symmetry in a charge configuration aids in predicting the positions where the net electric field might be zero.

Transcript

00:01 Hi everyone.

00:01 In this video, we're going to look at the concept of the electric field of a point charge.

00:07 And so we have a configuration that is a square, and we're going to be placing a third charge so that we get the electric field at this point a to be zero.

00:19 Okay, so we have a q here and a q here.

00:26 And they have the same magnitude.

00:28 And so we'll just call this q1 and q here.

00:30 So that we can track their electric fields a little easier.

00:36 Okay, so q1 is going to make an electric field that points straight up to a, and q2 is going to make an electric field that points along the diagonal.

00:50 So e2 is going to be like this.

00:53 All right, this is a square.

00:55 So these sides are all the same length, d, which is 0 .30 meters.

01:02 Okay.

01:06 And so that means our, let's just draw the electric fields over here.

01:11 So we have e1 like this.

01:14 We have e2 like this.

01:19 And then e2 has components e2 x, e2y, and this is 45 degrees.

01:34 Okay.

01:34 And so, in in order to make an electric field be zero, we need to have the e3x, exactly opposite e2x.

01:46 And then we need an e3y that goes down e2y plus another e1.

01:53 And so if we extend this down, what we're looking for is an e3 where this is e3y and e3x.

02:08 All right, so we want e3x plus e2x to be zero.

02:17 There is no e1x.

02:20 And then we want e3y plus e1 plus e2y.

02:30 That also has to add up to zero.

02:33 Ok, so let's compute some electric fields and see what we can find.

02:39 All right, so for q1, the distance between the q and the a, call that distance r, is equal to d.

02:52 And so e1 is k, q over r squared.

02:59 So e1 is 8 .99 times 10 to the 9 newton meter squared per kulum squared times qom, which is 7 microculems, so 7 .00, times 10 to the minus 6 koulogs divided by r squared and r is the 0 .30 meters and we need to square that.

03:26 So e1 ends up being 6 .99 times 10 to the 5th and that will be newtons per koum.

03:38 So there's one piece that we need.

03:41 Okay for q2 we can say that r squared is going to be d squared plus d squared.

03:55 So r squared is the 0 .30 meters squared plus 0 .30 meters squared.

04:06 So r squared ends up being 0 .180 meters squared.

04:14 All right, we can do e2y.

04:18 And so the electric field for charge 2, the y component, is going to be e2.

04:27 Times the sign of 45.

04:33 Okay, so e2y, and e2.

04:37 E2 is going to be kq2 over r squared, and then we have to multiply by sine 45.

04:45 E2y is 8 .99 times 10 to the 9, newton meter squared per kulam squared.

04:55 Q2 is the same seven microculems, and then we have a, sign 45 and we're defining by r squared which we found to be 0 .180 meters squared.

05:11 So e2y we get 2 .47 times 10 to the 5th newtons per coulop.

05:22 Okay so there's another piece of our puzzle.

05:26 Okay so now we need an e2x.

05:32 Well e2x is going in the negative of direction.

05:37 So we're going to have minus e2 cosine 45.

05:44 But the sign of 45 is equal to the cosine of 45.

05:49 So e2x is just minus e2y.

05:56 So e2x is minus 2 .6 is minus 2 .47 times 10 to the 5 newtons per coulomb...

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