A charge of +2.0 mC is located at x=0, y=0 and a charge of -4.0 mC is located at x=0, y=3.0 m .

step 1 All right, question 20 chapter 17. The question 20 says there are two charters and would like to

A charge of +2.0 mC is located at x=0, y=0 and a charge of...

A charge of $+2.0 \mathrm{mC}$ is located at $x=0, y=0$ and a charge of $-4.0 \mathrm{mC}$ is located at $x=0, y=3.0 \mathrm{m} .$ What is the electric potential due to these charges at a point with coordinates $x=4.0 \mathrm{m}, y=0 ?$

Key Concepts

Electric Potential

Electric potential is a measure of the work done per unit charge in bringing a test charge from infinity to a specific point in an electric field. It is expressed in volts and represents the potential energy per unit charge at that location.

Potential Due to a Point Charge

The electric potential due to an isolated point charge is calculated using the relationship V = kq/r, where V is the potential, k is Coulomb's constant, q is the charge, and r is the distance from the charge to the point of interest. This formula allows for determining how a single charge influences the electric potential in its surrounding space.

Principle of Superposition

The principle of superposition states that when multiple charges are present, the total electric potential at any given point is the algebraic sum of the potentials due to each individual charge. Since electric potential is a scalar quantity, each contribution is added without regard to direction.

Distance Calculation in Coordinate Geometry

Accurately determining the distance between charges and a point of interest is crucial when applying the electric potential formula. In a coordinate system, distances can be computed using the Pythagorean theorem, which is essential for finding the separation between points.

Transcript

00:01 All right, question 20 chapter 17.

00:06 The question 20 says there are two charters and would like to calculate the electric potential due to these two charge systems at a certain location away from them.

00:20 Okay, so to have a better understanding, let's have the cartesian coordinates, y axis and x axis like that.

00:31 All right so we have the first charge located at the center zero zero and let's call it q1 so q1 is a positive charge equals to three i'm sorry two positive two millicolums all right and located at zero zero the second charge is located at at 03 here.

01:01 That's the coordinates 0 ,03.

01:15 And let's call it q2.

01:16 So q2 is a negative chart, negative 4 milliculum.

01:22 The question is, find the electric potential at this point.

01:27 And this is basically for zero, the coordinates.

01:32 And by the way, all the dimensions here are measured in meters, means the point of our interest is four meters away from q1, four meters, and the two charges are three meters apart, three meters apart.

01:55 Okay, so the thing is, what is the electric potential at this point? all right, so the electric potential is determined or calculated by v is equal to constant k that's the formula times the magnitude of the charge causing the electric potential over the distance away from the charge right so here we got two charge points we have two charges all right and in this system the two charge is gonna affect the value of the electric potential at our point of interest and therefore we have to add the potential the total potential will be the the algebraic sum of the potential due to the first charge and potential due to the second charge.

02:45 And this is the plan.

02:47 So the total charge, as a matter of fact, is equal to the potential due to the first charge plus the potential due to the second charge.

02:59 Now remember, the electric potential is a scalar quantity, and therefore, when we include the charge in our calculations, we have to consider the sign of the charge...

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