Three point charges are located at the corners of an cquilateral triangle as in Figure P 15.13 .

Three point charges are located at the corners of an...

Key Concepts

Symmetry Considerations in Electrostatic Problems

Symmetry plays an important role in simplifying electrostatic calculations. In configurations where charges are arranged in symmetric patterns, such as in an equilateral triangle, the symmetry can reduce the complexity of the vector addition by canceling out certain components, thereby making it easier to determine the net force direction and magnitude.

Vector Addition of Forces

Since forces are vector quantities, determining the net force involves breaking down individual forces into their components and applying vector addition. This process requires considering both magnitude and direction, ensuring that the combined effect of various forces is accurately calculated.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged particles. It states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental for calculating the forces exerted by charged bodies on each other and underpins much of electrostatics.

Superposition Principle

The Superposition Principle in electrostatics states that the net force acting on any given charge is the vector sum of the individual forces exerted on it by all other charges. This principle allows for the analysis of complex charge configurations by considering each pair-interaction separately and then summing the contributions to obtain the overall force.

Transcript

00:01 For this problem on the topic of electric forces and fields, we are shown three point charges, each located at the corner of an equilateral triangle, as we have in the figure, and we want to find the magnitude and direction of the net electric force that is felt by the two microculeum charge.

00:19 Now we've placed the two microculeum charge at the origin in our diagram, and we can see that it feels a force f2 due to the seven microculem charge and a force ef2, and a force ef2.

00:30 F1 due to the minus 4 microculem charge.

00:33 So we first need to find the magnitudes of f1 and f2.

00:39 So f1 is equal to the electric constant k, which is 8 .99 times 10 to the 9, newton meter squared per coulomb squared, multiplied by the magnitude of the two charges, which is 2 times 10 to the minus 6 kouloms times 4 times 10 to the minus 6 cooloms, all divided by the square of the separation between these two charges, which is the side of the equilateral triangle 0 .5 meters squared, which gives us the magnitude of force f1 to be 0 .288 newtons.

01:33 Now similarly, the two microculem charge will feel a force f2 which again is k e 8 .99 times 10 to the 9 newton meter squared per coulomb squared times the product of charges 2 times 10 to the minus 6 cooloms multiplied by 7 times 10 to the minus 6 cooloms all divided by the square of the separation between the two charges 0 .5 meters squared, which gives us the magnitude of charge f2 to be 0 .503 newtons.

02:21 Now we can find the components of the resultant force that act on the 2 microculeum charge.

02:31 And so the horizontal component or x component of the resultant force acting on the 2 micraculum charge is equal to f1 minus the horizontal component of f2, which is which is f2 cosine of 60 degrees...

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