Calculate Resultant Force on Positive Charge in Rectangle with 4 Charges

[confused1]

Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1.3 m, b = 0.8 m, q = 1.8 × 10-9C)?

HELP: Use Coulomb's law and superposition.

HELP: Superposition tells us that we can find the force on the positive charge by looking at the negative charges one at a time. First find the force on the positive charge from just one of the negative charges, then from only the second negative charge, then from only the third negative charge. Then just "add" up these forces...remembering the vector nature of forces. (How do we "add" vectors?)

HELP: Coulomb's law is F=k(q1)(q2)/r2. Remember, however, that force is a vector so the magnitude of the total force will be the square root of the sum of the forces in the x-direction squared plus the sum of the forces in the y-direction squared. To determine the x- and y-component of the force notice that o ne charge exerts a force in the x-direction only, one charge exerts a force in the y-direction only, and one charge exerts a force that needs to be broken down into x and y components. When breaking the diagonal force down into x and y components, remember cosq = a/r and sinq = b/r.

 

[Astronuc]

Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1.3 m, b = 0.8 m, q = 1.8 × 10-9C)?

This would indicate all charges are + and given by q?

HELP: Use Coulomb's law and superposition.

Yes

HELP: Superposition tells us that we can find the force on the positive charge by looking at the negative charges one at a time. First find the force on the positive charge from just one of the negative charges, then from only the second negative charge, then from only the third negative charge. Then just "add" up these forces...remembering the vector nature of forces. (How do we "add" vectors?)

Well it applies to charge in general. Opposite charges (+ -) attract, like charges (+ +) or (- -) repel, but the magnitude of force would be the same dependent only on magnitudes of charges and distance of separation.

HELP: Coulomb's law is F=k(q1)(q2)/r2. Remember, however, that force is a vector so the magnitude of the total force will be the square root of the sum of the forces in the x-direction squared plus the sum of the forces in the y-direction squared. To determine the x- and y-component of the force notice that o ne charge exerts a force in the x-direction only, one charge exerts a force in the y-direction only, and one charge exerts a force that needs to be broken down into x and y components. When breaking the diagonal force down into x and y components, remember cosq = a/r and sinq = b/r.

That is one way, or one simply adds corresponding components of the vectors.

 

[quicknote]

I would approach this problem by first identifying the variables and using Coulomb's law to calculate the force between each pair of charges. Then, using superposition, I would add up these individual forces to determine the total force on the positive charge.

To start, I would label the charges and their respective positions on the rectangle:

q1 = -1.8 x 10^-9C (top left corner)
q2 = -1.8 x 10^-9C (top right corner)
q3 = -1.8 x 10^-9C (bottom right corner)
q4 = +1.8 x 10^-9C (bottom left corner)

Next, I would use Coulomb's law to calculate the force between each pair of charges. For example, the force between q1 and q4 would be:

F = (9 x 10^9 Nm^2/C^2)(-1.8 x 10^-9C)(1.8 x 10^-9C)/(1.3m)^2

Using this equation, I would calculate the force between each pair of charges and then break down the diagonal force into x and y components using the trigonometric relationships mentioned in the HELP section.

Once I have all the individual forces and their respective x and y components, I would use vector addition to add them up and determine the total force on the positive charge.

To summarize, as a scientist, I would approach this problem by using Coulomb's law and superposition to calculate the individual forces between each pair of charges and then use vector addition to determine the total force on the positive charge.