Three point charges are located at the corners of an equilateral triangle as shown in Figure P 2

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

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electric force between the 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 forms the foundation for calculating forces in electric charge systems.

Superposition Principle

The Superposition Principle in electrostatics means that the total force experienced by a charge is the vector sum of the forces exerted by each of the other individual charges. This principle allows for the calculation of net electric force in systems with multiple charges.

Vector Addition in Force Calculation

Vector Addition is the method used to combine forces considering both magnitude and direction. When forces are exerted at different angles, such as in the configuration of an equilateral triangle, vector addition must be used to accurately determine the net force acting on a charge.

Geometric Considerations in Charge Distribution

Geometric considerations involve using the positions of charges, such as the symmetry in an equilateral triangle, to simplify the analysis of forces. The known distances and angles in a regular geometric shape help in breaking down and accurately calculating the vector components of the forces between charges.

Transcript

00:01 So here we have three parts of the problem where we should first find the magnitude of the electric force, then the magnitude of the gravitational force and compare them to, and we actually need to find a for the part c the ratio of q over m in order for the magnitudes of the electric and gravitational force to be equal.

00:22 And this is a basic force problem where we have point.

00:29 This is on proton or in this case this is one this is one particle actually say this is a charged particle mp and the same exact particle mp where mp is the mass and we have forces electric force f e that is going against another force also electric force exactly the same f e and we have fg and fg that are these gravitational forces are always attracting and this in this case since the charges are plus e for both particles they are opposing and repelling each other so for the party we need to only solve for the force or the electrostatic force from the law which is k times the same q is present here, so q squared over r squared and r is the distance between them.

01:57 So we can substitute this values and say this is 8 times 988 times 10 to the 9 power and then 1 .6 times 10 to the minus 19 squared over 3 .8 times 10 to the negative 10 power squared and this equals to 1 .59 times 10 to the negative 9 power mutants.

02:33 So this is for the part a for the part b we should repeat this using the gravitational force formula which is fg equals g this is the big gravitational constant times masses and these are these are masses of one proton then over the square of the radial distance between them and we can substitute the known values here to obtain 6 .67 times 10 to the negative 11 power times ratio of 1 .67 times 10 to the negative 27 power this goes squared 3 .8 times 10 to negative 10 power squared and this is equal to 1 .29 times 10 to the negative 45th power muses.

03:42 So extremely weaker force when comes to gravity, tens of orders of magnitude.

03:51 So for the part c basically, when will this force equal? well, we should seem to equate their expressions...

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