Three point charges are placed on the x-y plane: a+50.0-n C...

Three point charges are placed on the $x-y$ plane: $a+50.0-n C$ charge at the origin, a $-50.0-\mathrm{n} \mathrm{C}$ charge on the $x$ axis at $10.0 \mathrm{~cm}$, and $\mathrm{a}+150 \mathrm{n} \mathrm{C}$ charge at the point $(10.0 \mathrm{~cm}, 8.00 \mathrm{~cm})$. (a) Find the total electric force on the $+150$ $\mathrm{n} \mathrm{C}$ charge due to the other two. (b) What is the electric field at the location of the $+150-\mathrm{n} \mathrm{C}$ charge due to the presence of the other two charges? Example $16-4$

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrical force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance that separates them. This law is a cornerstone in electrostatics and applies regardless of the specific arrangement of charges.

Electric Force

The electric force is the interaction between electrically charged objects. In the context of point charges, the direction and magnitude of the force are determined by the charges’ magnitudes, their signs, and the separation distance. This concept explains how charged particles influence each other by either attracting or repelling one another.

Electric Field

The electric field is a vector field that represents the influence a charge exerts in the space around it. It is defined as the force experienced per unit positive charge placed at a point in space. The concept of the electric field is fundamental in understanding and predicting the behavior of charges in an environment.

Superposition Principle

The Superposition Principle states that when multiple charges are present, the net electric force or field at a point is the vector sum of the individual forces or fields produced by each charge independently. This principle simplifies the analysis of complex arrangements of multiple charges by allowing separate computation of each contribution.

Vector Addition

Vector Addition is the process of combining multiple vectors to determine a resulting vector in both magnitude and direction. In the study of forces and electric fields, it is crucial because these quantities have both size and direction, and their combined effect is found by summing their individual vector components.

Transcript

00:01 For this problem on the topic of electrostatics, we have three point charges placed on the xy plane, a 50 nanoculum charge at the origin, a minus 15 nanoculum charge on the x axis at a distance of 10 centimeters, and a 150 nanoculum charge at the point 10 centimeters and 8 centimeters.

00:18 We want to find the total electric force on the 150 nanoculum charge due to the other two, and the electric field at the location of the 150 nanoculum charge due to the presence of the other two charges.

00:30 Now the x component of the electric force acting on q3 is due to the force of q1 and q3 because the charges have the same sign the force is repulsive in the positive x direction.

00:42 The y component of the electric force on q3 due to q1 is also repulsive so it acts in the positive y direction however the y component of the force due to q2 is attractive since the charges of opposite signs thus the y component of the force of q2 on q3 acts in the negative y direction.

01:00 Feel at the location of q3 due to the other two charges is equal to the net electric force on q3 divided by q3.

01:09 So firstly to find the x component of the net force on three, this is the net force that one, or the force that one exerts on three in the x direction, plus the force that two exerts on three in the x direction, which is positive k times the magnitude of q1 times the magnitude of q3 divided by the separation between 2r13 squared times the cosine of theta plus 0.

01:56 Putting in our values, this is 8 .99 times 10 to the power 9 newton meter squared per coulomb squared times 50 times 10 to the minus 9 couloms times q3, which is 150 times 10 to the minus 9 couloms, all divided by 0 .1 meters squared plus 0 .08 meters squared and multiplied by the cosine of theta which is 0 .1 meters divided by the square root of 0 .1 meters squared plus 0 .08 meters squared and so calculating we get the force that the net force on 3 in the x direction to be 0 .00 3 to newton's to two significant figures...

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