Two point charges are located on the y -axis as follows:...

Two point charges are located on the $y$ -axis as follows: charge $q_{1}=-1.50 \mathrm{nC}$ at $y=-0.600 \mathrm{~m},$ and charge $q_{2}=+3.20 \mathrm{nC}$ at the origin $(y=0) .$ What is the total force (magnitude and direction) exerted by these two charges on a third charge $q_{3}=+5.00 \mathrm{nC}$ located at $y=-0.400 \mathrm{~m} ?$

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges as being directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating the magnitude and direction of the electric force between any two charges.

Superposition Principle

The Superposition Principle states that the total force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge separately. This principle allows us to analyze complex systems by considering pairwise interactions between charges.

Vector Addition

Vector Addition is used to combine forces that have both magnitude and direction. When calculating the force on a charge due to other charges, each force is a vector, and their sum must account for both horizontal and vertical components, although in collinear arrangements, this process reduces to careful consideration of the sign and magnitude along the line.

Transcript

00:01 So we know that from the columns law the force between two charges is given by cuban killed to divert our square.

00:09 We're case proportionally constant and it is given by 8.987 double five multiplied by 10 to the power nine newton meters square per square and the cuban two charges and the small artist separation between them.

00:26 So now magnitude of f one between cuban and q three can be written.

00:31 Sk cuban q three verbs are square.

00:35 Where are will be equals two by three minus y one.

00:39 So we have values of y three s, minus 0.4 m and raven as minus 0.6 m.

00:50 Okay, so from here are comes out to be 0.2 m.

00:54 So now, putting all the values in this equation to get there from so f one will be close to eight point 987 double five multiplied by 1.5 player by 10 to the power minus.

01:07 And we are taking magnitude of the charges only and multiplied by five multiplied by 10 to the power minus nine column and the stands his 0.20 point 2 m square.

01:19 So from here comes out to be 1.685 multiplied by 10 to the power minus six.

01:26 This force will be directed into negative y direction, so i am writing minus white cap.

01:33 Similarly, the force f two between q two and q three can be written as q two q three rs were and the distance between two and three will be the distance between okay.

02:00 Q two q three divided by r squared the distance between charges two and three artists are will be equals two y three minus two, and we have values by three calls to minus 0.4 and y two equals two jiro nitta.

02:19 So from here r is equal to minus 0.4 m.

02:23 Okay, so now i have two is equal to 8.987 double five multiplied by q two is 3.2, multiplied by 10 to the power minus nine q and q three is five multiplayer bait and to the power minus nine, and the distance between them is minus 0.4, so minus 0.4 m square...

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