A charge of -3.00 nC is placed at the origin of an x-y coordinate system, and a charge of 2.00 n

A charge of -3.00 nC is placed at the origin of an x-y...

Key Concepts

Vector Addition

Vector addition is the process of combining two or more vectors to produce a resultant vector. When calculating the net force in electrostatics, each component of the force from different charges is added together using vector addition methods, often involving trigonometry to determine the magnitude and direction of the resultant force.

Vector Decomposition

Vector decomposition involves breaking a force into its perpendicular components, usually along the x- and y-axes. This process is essential in problems involving forces because it simplifies the calculation of the net force by dealing with each Cartesian component separately.

Superposition Principle

The superposition principle in electrostatics states that the total force acting on a charge is the vector sum of the forces exerted by each of the other individual charges independently. This allows for the analysis of complex charge configurations by calculating the net force as the combination of multiple simpler forces.

Electric Force

The electric force is the interaction between charged objects, governed by Coulomb's Law. It can be attractive or repulsive depending on the signs of the charges, and it acts along the line joining the centers of the two charges. Understanding this force is crucial for analyzing how charges influence each other in an electric field.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This fundamental relation helps in calculating the interactions between charged particles in an electric field.

Transcript

00:01 In this question, we have a charge of negative 3 nanoculum placed at the origin, and then a charge of 2 nanoculums placed on the y -axis at a distance of 4 centimeters from the origin.

00:13 And then in the first part of the question, part a, we're asked to find the x and y components of the total force exerted on a new charge, a third charge of five nanoculums if it's placed at x equals 3 and y equals.

00:31 Four.

00:32 So to begin tackling this problem, let's first kind of think about the direction of the electric force on that third charge, that green charge, which i've drawn here in my diagram.

00:48 So the electric force is always going to act along the line that's connecting the two charges.

00:55 So for example, with the red and green charge, it's going to be this line right here.

01:02 And since the red charge is negative and the green charge is positive, that means we're going to have an electric force on the green charge directed along this direction.

01:16 So it's attracted towards that negative charge at the origin.

01:23 And then similarly, we're also going to have a force from the blue charge on the green charge.

01:30 And that's also going to act along the line connecting.

01:33 Those two charges, which is just a horizontal line.

01:37 But this time the force is going to be a repulsive force because those two charges are both positive.

01:45 And so the force from the blue charge is going to be acting towards the right here.

01:50 So we can see that in the x direction, both of the charges are acting in some way.

01:58 In the y direction, we only have the force from the negative charge, having an effect.

02:06 So let's go ahead and find the components of the various forces that are acting on the charge.

02:14 So from the two nanoculum charge, we've got kq1, q2 over r squared.

02:30 So of course, k is 9 times 10 to the 9.

02:35 That's just a constant.

02:37 And then for q1, let's go ahead and use the two nanoculum.

02:42 So that's two times 10 of the minus nine couloms.

02:46 And then multiply that by the other charge, which is five.

02:55 And then the r should be the distance between them.

02:57 And it should be in standard units of meters.

02:59 So if it's three centimeters, it's 0 .03 meters.

03:03 And that's all squared.

03:11 So once we go through the actual calculation there, that gives us 1 times 10 to the minus 4 newtons for the magnitude of that force.

03:22 And of course, that's all in the y direction.

03:25 So later on when we get to the total force, we can just add that to the y component of the total force.

03:32 And then let's go ahead and calculate what the magnitude of the red force is, the one from the negative three nanoculums.

03:44 So that's going to be the exact same calculation, except we're going to use three nanoculums for the one charge.

03:55 And also a distance or a separation of five centimeters.

04:04 Okay, that's just using pythagorean theorem.

04:09 If you've got a right angle triangle and the two sides that are not, the hypotenuse are four and three, then the hypotenous is going to be five.

04:15 Okay, so i'm using 5 centimeters for my r.

04:24 So following through with that calculation, we would get a magnitude of 5 .4 times 10 to the minus 5 newtons for that.

04:33 Now, of course, that's the total magnitude of this, the force from the negative charge.

04:38 We do need to split that into components because we can see from the diagram that that red force is acting in both the x direction and the y direction.

04:48 If we know what this angle is here, then we can just go ahead and calculate those components pretty easily.

04:56 So to get that angle, i'm just going to use tan theta is equal to opposite over adjacent, which is 4 over 3...

Please give Ace some feedback