Finding charge based on net force and other charges

In summary, the net electric force on the blue sphere, with a positive q charge at the origin, is directed in the -y direction and has a magnitude F. A red charge with unknown positive charge q_red is located at (d1,0) and a yellow charge with a negative 2q charge is located at (d2cos(theta),-d2sin(theta)). Given that the magnitude of the charge on the yellow sphere is determined to be 2q, the charge q_red on the red sphere can be calculated using the equation: q_red = (2q*d1^2*cos(theta)) / d2^2, where q represents the charge on the blue sphere, d1
  • #1
jelliDollFace
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Homework Statement



Blue charge is at origin with positive q charge
Red charge at point (d1,0) with unknown positive charge q_red
Yellow charge at point (d2cos(theta),-d2sin(theta)) with negative 2q charge

The net electric force on the blue sphere has a magnitude F and is directed in the - y direction.

Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q. Calculate the charge q_red on the red sphere. Express your answer in terms of q, d1, d2, and theta.

Homework Equations



electric force F = kq_1q_2/r^2 where k = 9*10^9, q_1 and q_2 represent point charges, and r is distance between point charges

The Attempt at a Solution



F = [(k*q_yellow*q_blue)/d2^2 ] + [(k*q_red*q_blue)/d1^2]
F = [(k*(-2q)*q)/d2^2] + [(k*q_red*q)/d1^2]
d1^2[F - ((k*(-2q)*q)/d2^2)] / kq = q_red

i think I'm on the right track but i did not use theta which i need to, where did i go wrong
 

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  • #2
does this involve the coordinate location of the yellow charge because it contains theta which i think i need in my final answer, but the distance is stated as d2 so why should i need it?
 
  • #3
jelliDollFace said:

Homework Statement



Blue charge is at origin with positive q charge
Red charge at point (d1,0) with unknown positive charge q_red
Yellow charge at point (d2cos(theta),-d2sin(theta)) with negative 2q charge

The net electric force on the blue sphere has a magnitude F and is directed in the - y direction.

Suppose that the magnitude of the charge on the yellow sphere is determined to be 2q. Calculate the charge q_red on the red sphere. Express your answer in terms of q, d1, d2, and theta.

Homework Equations



electric force F = kq_1q_2/r^2 where k = 9*10^9, q_1 and q_2 represent point charges, and r is distance between point charges

The Attempt at a Solution



F = [(k*q_yellow*q_blue)/d2^2 ] + [(k*q_red*q_blue)/d1^2]
F = [(k*(-2q)*q)/d2^2] + [(k*q_red*q)/d1^2]
d1^2[F - ((k*(-2q)*q)/d2^2)] / kq = q_red

i think I'm on the right track but i did not use theta which i need to, where did i go wrong

I can't see your picture as yet, but I would suggest that you separate the forces into their x,y components and then add them. They tell you the result vector is acting in the -Y direction only, so x components must add to 0. Force is a vector and adding the magnitudes if they are not acting along the same line is not the way to do it.
 
  • #4
how about this, i put the net forces into components:

fnet_x = [k(2q)(q)/(d2cos(theta))^2] + [k(q_red)(q)/(d1^2)]
fnet_y = [k(2q)(q)/(d2sin(theta))^2] + 0

F = sqrt((fnet_x)^2 + (fnet_y)^2)
[sqrt[F^2 - (fnet_x)^2](d2sin(theta))]/(2q)(k) = q_red

is that correct now?

how do i factor in the -y net force direction?
 
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  • #5
jelliDollFace said:
how about this, i put the net forces into components:

fnet_x = [k(2q)(q)/(d2cos(theta))^2] + [k(q_red)(q)/(d1^2)]
fnet_y = [k(2q)(q)/(d2sin(theta))^2] + 0

F = sqrt((fnet_x)^2 + (fnet_y)^2)
[sqrt[F^2 - (fnet_x)^2](d2sin(theta))]/(2q)(k) = q_red

is that correct now?

how do i factor in the -y net force direction?

Not quite.

First simply identify the force between the Blue/Red and the Blue/Yellow.
These are the forces that you must treat as vectors.

Hence
F(b/r) = kqb*qr/(d1)2*x-hat + 0*y-hat
F(b/y) = kqb*qy/(d2)2*Cosθ*x-hat + kqb*qy/(d2)2*Sinθ*y-hat

Now when you add F(b/r) and F(b/y) you add the components.
But you also know that the x-components (x-hat terms) must add to 0
And you also know that the charge on Yellow is -2*q and the charge on Blue is +1*q. The qr is the one that is unknown. Figure it must be a positive charge since Red is positive Yellow negative and otherwise they could never add to 0.
 
  • #6
so this is what i got, since we know the x components must sum to zero soo...

[(q_red)(+q)k]/d1^2 + [(+q)(-2q)k]/d2cos(theta)^2 = 0
so q_red = [-k(+q)(-2q)(d1^2)]/[(d2cos(theta)^2)(+q)(k)]

is this right?
 
  • #7
jelliDollFace said:
so this is what i got, since we know the x components must sum to zero soo...

[(q_red)(+q)k]/d1^2 + [(+q)(-2q)k]/d2cos(theta)^2 = 0
so q_red = [-k(+q)(-2q)(d1^2)]/[(d2cos(theta)^2)(+q)(k)]

is this right?

No. I don't think you read the equations I gave you carefully.

[tex] \vec{F_{BR}} = \frac{k*Q_B*Q_R}{d_1^2} *\hat{x} + 0*\hat{y}[/tex]

[tex] \vec{F_{BY}} = \frac{k*Q_B*Q_Y}{d_2^2}*Cos\theta* \hat{x} + \frac{k*Q_B*Q_Y}{d_2^2}*Sin\theta *\hat{y} [/tex]
 
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  • #8
okay i see now, aside from the issue with the sine and cosine, was my approach for solving for q_red correct?

here it is with corrections

[(q_red)(+q)k]/d1^2 + [(+q)(-2q)(k)(cos(theta))]/d2^2 = 0

q_red = -[k(+q)(-2q)(d1^2)(cos(theta))]/[(d2^2)(+q)(k)]

q_red = -[(-2q)(d1^2)(cos(theta))]/[(d2^2)] = (2q)(d1^2)(cos(theta))]/[(d2^2)

how about now?
 
  • #9
jelliDollFace said:
okay i see now, aside from the issue with the sine and cosine, was my approach for solving for q_red correct?

here it is with corrections

[(q_red)(+q)k]/d1^2 + [(+q)(-2q)(k)(cos(theta))]/d2^2 = 0

q_red = -[k(+q)(-2q)(d1^2)(cos(theta))]/[(d2^2)(+q)(k)]

q_red = -[(-2q)(d1^2)(cos(theta))]/[(d2^2)] = (2q)(d1^2)(cos(theta))]/[(d2^2)

how about now?

That looks more like it.
 
  • #10
thanks so much, it was right!
 

1. What is charge and how is it measured?

Charge is a fundamental property of matter that determines its electromagnetic interactions. It can be measured in units of coulombs (C) using an instrument called an electrometer.

2. How does the net force affect the charge of an object?

The net force acting on an object is directly proportional to its charge. This means that the greater the net force, the greater the charge of the object will be.

3. Can the charge of an object change due to the presence of other charges?

Yes, the charge of an object can change due to the presence of other charges. This is known as charging by induction, where the presence of a charged object causes a redistribution of charges on the object being charged.

4. How do you determine the charge of an object based on the net force and other charges in the system?

To determine the charge of an object, you can use Coulomb's Law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. By rearranging this equation, you can solve for the charge of the object.

5. What factors can affect the accuracy of finding charge based on net force and other charges?

The accuracy of finding charge based on net force and other charges can be affected by factors such as the precision and calibration of the instruments used, the distance between the charges, and any external forces or interference that may be present in the system.

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