Four identical charged particles (q=+10.0 μC) are located on the corners of a rectangle as shown

Four identical charged particles (q=+10.0 μC) are located on...

Key Concepts

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges. It states that the magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them, with a constant of proportionality that depends on the medium. This law is fundamental in calculating interactions in electrostatics.

Principle of Superposition

The principle of superposition asserts that when multiple charges contribute to the electric force on a given charge, the total force is the vector sum of the individual forces exerted by each charge. This approach allows the analysis of complex charge configurations by evaluating pairwise interactions.

Vector Addition in Electrostatics

In electrostatics, forces are vector quantities, which means they have both magnitude and direction. Accurately determining the net force involves decomposing individual forces into their components along chosen coordinate axes and then adding these components together. This process is essential for understanding the resultant effect of multiple forces acting at various angles.

Symmetry Considerations

Symmetry considerations help simplify the analysis of electric forces by reducing the complexity of the problem. Recognizing symmetrical arrangements in charge configurations often allows for certain force components to cancel out, streamlining the computation of the net force.

Transcript

00:01 We have in this question four identical charges being arranged in a rectangle and we want to find what is the force acting on the bottom left corner charge which is this particular charge due to the other three charges so the force due to the three other charges that's acting on this particular charge now we know that the force electric force is given as kq1 q2 over r square.

00:36 In this case the q1 and q2 are both 10 microcholomes so they are the same and the only thing that's difference will be the r square, the distance away and because they are at an angle, right, there will be some components vertical and horizontal components.

00:58 So taking the axis to be as such, right x and y we will need to split up the force that's coming from this diagonal charge over here into the x and y component in order to add them up together so the charge coming from let's say let me call this charge 1 2 and 3 so from 1 and 3 they are both along the axis 1 will result in a force in the along the y axis 3 where you result in the force along the x -axis but for two it'll be both in the y and x -axis some combination of both so the easiest one i'm going to start off with one label this is f1 i forced due to the charge one is k times 10 microchromes square distance is 15 centimeters so 0 .15 meters and we get 40 newtons.

02:19 Now we know that this force will be acting in the negative y -axis because it's repulsive.

02:26 So this is negative j hat.

02:34 For the f3, this is k10 microchrome square.

02:39 Distance apart is 60 centimeters, so there's 0 .6 square.

02:45 Don't forget to square the distance as well.

02:48 Right and we should get 2 .5 newtons and the negative x direction so negative i had now for f2 this one slightly trickier we will have to consider the angle over here theta let me just call this theta which extends out as such so there's theta right the force will be in this direction f2 but it will have a horizontal and vertical component and so this the vertical sorry this is the horizontal this is the vertical for the horizontal component just call this fx f2x to be equals to f2 times cosine and because it's in the negative direction you mean negative i had what is f2? well f2 is just k, 10 microchromes square.

04:16 If other about the distance.

04:18 In this case the distance is 0 .15 square plus 0 .6 square.

04:25 Right by pythagall steyer.

04:29 What is cosine theta? well, cosine theta we can use the right angle triangle over here.

04:37 This right angle triangle.

04:38 Go.

04:39 So cosine theta will be just adjacent over hypotenous.

04:42 Adjacent is this length, 60 centimeters, hypotenuse square root soft, 0 .6 square plus 0 .15 squared squared...