The three charges shown at right are located at the vertices of an isosceles triangle. Calculate

The three charges shown at right are located at the vertices...

Key Concepts

Electric Potential

Electric potential is a measure of the work done per unit charge to bring a small positive test charge from infinity to a given point in an electric field. It is a scalar quantity which means that contributions from multiple charges can be algebraically added. In problems involving point charges, the potential due to each point charge is calculated individually and then summed to find the net potential at the point of interest.

Superposition Principle

The superposition principle states that in a system of multiple charges, the total electric potential at any point is the algebraic sum of the potentials due to each charge considered independently. This principle greatly simplifies the analysis of complex systems since the contributions of each charge do not interfere with one another.

Coulomb's Constant and Coulomb's Law

Coulomb's constant (commonly denoted as k, approximately 8.99×10^9 N·m²/C²) is a key factor in Coulomb's Law, which quantifies the electrostatic force between two point charges. When calculating the electric potential due to a point charge, Coulomb's constant is used in the formula V = kQ/r, where Q is the charge and r is the distance from the charge to the point of interest.

Geometric Analysis in Charge Configurations

In problems involving charges arranged in geometrical shapes, such as triangles, it's important to use geometry to determine the distances between the charge positions and the point where the potential is calculated. Analyzing the configuration, such as finding midpoints or using triangle properties, is crucial to accurately applying the formulas for electric potential.

Transcript

00:01 So this question can be very tricky, but the key to it is that you're dealing with the triangle.

00:06 So the distance between the positive charge and the negative charge is 4 centimeters, and the distance between the negative charges is 2 centimeters.

00:15 And the question asks to find the electric potential at the midway point of the base.

00:21 So the proper equation to use is this form of the electric potential, which is v is equal to kc, the kulom constant, which i have.

00:31 Have right here times the charge q divided by are the distance between the charge and the point.

00:40 So the question wants to find again the electric potential at the midway point of the base.

00:46 So from the positive charge all the way down right up there, that's the midway point.

00:53 And if you look closely, that creates a triangle.

00:56 So if you go over here to this side, you'll look at the triangle.

01:04 So the hypotenuse is four centimeters.

01:06 The bottom the base that's halfway point so that's one centimeter and in the distance what we're looking for is r so this just becomes the pythagrin theorem so you have r squared plus one squared is equal to four squared so one squared is one four squared is sixteen to get rid of the one you subtract it to both sides so you have r squared is equal to 15 solving for r you get r is equal to the square root of 15 which is 3 .8 centimeters and for this question you want centimeters to be meters since i have the conversion over here to go from centimeters to meters so you divide by a hundred so our r becomes point zero three meters so now from here all you have to do is make sure you plug in the correct numbers to find the electric potential for each charge.

02:21 So for the positive charge, we'll call that v1.

02:24 The bottom left we'll call v2 and bottom right v3.

02:33 So let's look at v1.

02:37 Okay, you see the kulum constant, 8 .98 times 10 to the ninth times the charge q...

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