Component Force on a 1.0 nC Charge

In summary, the conversation is about finding the force on a 1.0 nC charge at the bottom of a figure, given the presence of other charges at specific distances and angles. The first equation listed is used to calculate the total force, and the x and y components are determined using trigonometric functions. The placement of the particles is unclear, but the correct values for the x and y components have been obtained by plugging in the given charges and distances. More details of the calculations would be helpful for further understanding.
  • #1
Physistory

Homework Statement


What is the force F on the 1.0 nC charge at the bottom in the figure? Give your answer in component form.

In the figure, the +!.0 nC charge is adjacent to a +2.0 nC charge to the left at a 45° angle, a -6.0 nC charge directly above, and a -2.0 nC charge to the right at a 45° angle. Both distances between the first and third charges adjacent to the 1.0 nC charge are 5.0 centimeters in length.

Homework Equations



F = F2on1 + F3on1 + F4on1 = (K)(q1)(q2)/(r2)

x2 + y2 = z2; x2 = z2 - y2

C = (pi)*r2 = (pi)*(5)2 = 78.5 cm
C/4 = (19.6 cm)/2 = 9.81 cm

The Attempt at a Solution


I foremost determined the direction of the net force to be somewhere between east and northeast of the 1.0 nC charge (hereafter denoted q1 and the other charges so forth). I have assumed this because q2 would repel q1, while q3 and q4 would attract it. Thus, q1 would be pulled more up and eastward than it would be pulled southeastward. In contrast, q1 would only be pulled directly upward, in the direction of q3 if q4 were positive, because q2 and q4 would then be canceled out.

Using the first equation listed above, I added the forces and obtained a total force of 3.6*10-5 N. The three values I added to obtain this number were 7.2*10-6, 2.16*10-5, and 7.2*10-6 N again.

On my first attempt, I thought that to solve for the x-component I merely had to multiply each force by their respective cosines. In doing so, I obtained the values 5.09*10-6, 2.16*10-5 and 5.09*10-6 N which added to 3.17*10-5 N. This was not correct.

The value 2.16*10-5 was also obtained by plugging q1, q3 and 5.0 cm into the first equation. My textbook lists this (or precisely, 2.2, which is very close to 2.16) as the correct value for the y-component of the force. I believe that I understand why (that is, the direction from q1 to q3 is up and can therefore be found just by plugging in the two charges and the distance between them).

I am as yet unsure how to solve for the x-component. I have tried using Pythagoras' equation with multiple value combinations, but have not yet obtained anything close to the correct value, which my textbook lists to be 1.02*10-5 N. I would be very grateful for any hints as to whether there is something I am overlooking or am failing to realize. Thank you in advance!
 
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  • #2
Physistory said:
In the figure, the +!.0 nC charge is adjacent to a +2.0 nC charge to the left at a 45° angle, a -6.0 nC charge directly above, and a -2.0 nC charge to the right at a 45° angle. Both distances between the first and third charges adjacent to the 1.0 nC charge are 5.0 centimeters in length
Just stating the angle is ambiguous. Are the ±2nC charges both also "above"?
Physistory said:
I added the forces and obtained a total force of 3.6*10-5 N.
Please show your working, and keep it all symbolic. Avoid plugging in numbers until the final step.
Force is a vector. Forces in different directions must be added accordingly. Without seeing your working or going through the calculation myself I cannot tell if you did that correctly.
 
  • #3
I'm not sure that I understand the placement of the particles. Based on your numbers that your are calculating I'm guessing it is as shown.
upload_2017-8-6_17-4-9.png

As haruspex noted, you should show more detail of your calculations.

Physistory said:
Using the first equation listed above, I added the forces and obtained a total force of 3.6*10-5 N. The three values I added to obtain this number were 7.2*10-6, 2.16*10-5, and 7.2*10-6 N again.
You don't want to add the magnitudes of the three forces since they don't point in the same direction.

On my first attempt, I thought that to solve for the x-component I merely had to multiply each force by their respective cosines. In doing so, I obtained the values 5.09*10-6, 2.16*10-5 and 5.09*10-6 N which added to 3.17*10-5 N. This was not correct.
What is the x component of the force between the 1 nC and the -6 nC charge?

The value 2.16*10-5 was also obtained by plugging q1, q3 and 5.0 cm into the first equation. My textbook lists this (or precisely, 2.2, which is very close to 2.16) as the correct value for the y-component of the force. I believe that I understand why (that is, the direction from q1 to q3 is up and can therefore be found just by plugging in the two charges and the distance between them).
That looks right if the particles are arranged as shown above. But, it would be helpful to us if you showed more details of your calculations.
 

Related to Component Force on a 1.0 nC Charge

1. What is component force?

Component force refers to the individual forces acting on an object in a particular direction. In the case of a 1.0 nC charge, it is the force acting on the charge due to the presence of other charges in its surroundings.

2. How is component force on a 1.0 nC charge calculated?

The component force on a 1.0 nC charge is calculated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. Why is the charge specified as 1.0 nC?

The charge is specified as 1.0 nC (nanoCoulombs) because it is a commonly used unit in describing small quantities of electric charge. One nanoCoulomb is equal to 10^-9 Coulombs.

4. How does the distance between charges affect the component force?

The distance between charges has an inverse relationship with the component force. As the distance increases, the force decreases and as the distance decreases, the force increases. This is because the force is spread out over a larger area as the distance increases, resulting in a weaker force.

5. Can the component force on a 1.0 nC charge be negative?

Yes, the component force on a 1.0 nC charge can be negative if it is being repelled by another charge with the same sign. This indicates that the force is acting in the opposite direction of the charge's motion.

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