Three point charges are aligned along the x axis as shown in Figure P 23.52 . Find the electric

Three point charges are aligned along the x axis as shown in...

Key Concepts

Coordinate System

A coordinate system helps in specifying positions in space and is particularly useful in electrostatic problems for defining the locations of charges and points of interest. It allows for a systematic approach in breaking down vector components and analyzing the directions and magnitudes of the electric field along different axes.

Vector Addition

Vector addition is crucial when combining electric field contributions from multiple charges, as each electric field is a vector. Properly adding these vectors involves breaking them into components, summing each component separately, and then recombining them to obtain the total electric field at a point.

Superposition Principle

The superposition principle states that the total electric field at any given point due to multiple charges is the vector sum of the electric fields produced by each charge individually. This concept is essential for solving problems with several point charges, as it allows one to handle complex charge distributions by considering one charge at a time.

Electric Field

The electric field is a vector quantity that represents the force per unit charge experienced by a small positive test charge placed in the vicinity of other charges. It provides a way to describe the influence that charges exert on each other through space, and its calculation involves considering both magnitude and direction.

Coulomb's Law

Coulomb's Law describes the force between two point charges, stating that the magnitude of the electrostatic force between them is proportional to the product of their charges and inversely proportional to the square of the distance separating them. This law forms the basis for determining the electric field produced by individual point charges and is critical in any calculation involving electrostatic interactions.

Transcript

00:01 In this problem on the topic of electric fields, we have three point charges that are aligned along the x -axis, as we can see in the figure.

00:08 We want to find the result of the electric field at the position 2 -0, and then at the position 0 -2.

00:16 Now, the field e1, due to the 4 nanoculum charge, is in the minus x direction.

00:26 And so, e1 is equal to the electric constant k -e times the magnitude of the charge cube.

00:35 Times the distance to the point in question r squared along direction r hat.

00:44 And so this is equal to 8 .99 times 10 to the 9 newton meter squared per coulom squared multiplied by the charge minus 4 times 10 to the minus 9 quoloms divided by its distance, which is 2 .5 meters squared and this is in the i -hat direction.

01:21 And so this gives us minus 5 .75 i -hat newton's a coulom.

01:33 And so likewise we can find the field e2 and e3 due to the 5 nanoculum and 3 charges respectively.

01:43 And so e2 is equal to, again, k .e times q over r squared, r hat, which is 8 .99 times 10 to the 9, newton meter squared per coulomb squared times the charge of 5 nanocoloms of 5 times 10 to the minus 9 couloms, all divided by 2 meters, squared and that's in the i -hat direction this gives us e2 to be 11 .2 newtons per coulom along direction i -hat and for the third charge we have the electric field e3 is again equal to 8 .99 times 10 to the 9 newton meter squared per koolom squared times a charge of 3 times 10 to the minus 9 couloms divided by a distance of 1 .2 meters squared and this as well is a long unit vector i hat this gives us e3 to be 18 .7 newtons per kulum i hat and so therefore the net electric field at the point to 0, we'll call it er, the resultant electric field is e1 plus e2 plus e3.

03:45 And all of these are in the same direction, so we can simply add the magnitudes, and that is 24 .2 neutrons per kulum in the positive.

04:00 X direction.

04:06 And so that's the resultant field at two zero...

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