Find the unknown charges q1 and q2

In summary, the electric field at point A is shown to be E = Exi + Eyj. The unknown charges are q1 and q2.
  • #1
JessieS
4
1

Homework Statement


The geometrical positions of point-like charges and point A situated in the xy-plane in terms of the length parameter a. The vector of electric field E at point A is shown schematically and measured as E = Exi + Eyj (that is, both Ex and Ey are given). If possible, find the unknown charges q1 and q2.

**E_2 is the electric field with respect to q2. Not shown in figure. **
**E_1 is the electric field with respect to q1. (Same direction as E) **

**k_e is Coulomb's constant.**

Screen Shot 2016-06-26 at 2.40.14 PM.png


Homework Equations


E[/B] = Exi + Eyj
Ex = E_1*cos(45°) - E_2*cos(45°)
Ey = E_1*sin(45°) + E_2*sin(45°)
E = F/q = (k_e*q)/r^2

The Attempt at a Solution


E_1 [/B]= (k_e*q1)/(2a)^2 = (k_e*q1)/(4a^2)

E_2 = (k_e*q2)/(2a)^2 = (k_e*q2)/(4a^2)

Ex = (E_1 - E_2)*2/sqrt(2)

Ey = (E_1 + E_2)*2/sqrt(2)

E
= 2/sqrt(2)*(E_1 - E_2) i + 2/sqrt(2)*(E_1 + E_2) j = 2/sqrt(2)*(k_e/(4a^2))*(q1 - q2) i + 2/sqrt(2)*(k_e/(4a^2))*(q1 + q2)I am stuck here; I'm not sure if I've been going about this correctly or what steps to take next.

Thank you.
 
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  • #2
JessieS said:

Homework Statement


The geometrical positions of point-like charges and point A situated in the xy-plane in terms of the length parameter a. The vector of electric field E at point A is shown schematically and measured as E = Exi + Eyj (that is, both Ex and Ey are given). If possible, find the unknown charges q1 and q2.

**E_2 is the electric field with respect to q2. Not shown in figure. **
**E_1 is the electric field with respect to q1. (Same direction as E) **

**k_e is Coulomb's constant.**

View attachment 102522

Homework Equations


E[/B] = Exi + Eyj
Ex = E_1*cos(45°) - E_2*cos(45°)
Ey = E_1*sin(45°) + E_2*sin(45°)
E = F/q = (k_e*q)/r^2

The Attempt at a Solution


E_1 [/B]= (k_e*q1)/(2a)^2 = (k_e*q1)/(4a^2)

E_2 = (k_e*q2)/(2a)^2 = (k_e*q2)/(4a^2)

Ex = (E_1 - E_2)*2/sqrt(2)

Ey = (E_1 + E_2)*2/sqrt(2)

E
= 2/sqrt(2)*(E_1 - E_2) i + 2/sqrt(2)*(E_1 + E_2) j = 2/sqrt(2)*(k_e/(4a^2))*(q1 - q2) i + 2/sqrt(2)*(k_e/(4a^2))*(q1 + q2)

I am stuck here; I'm not sure if I've been going about this correctly or what steps to take next.

Thank you.
Hello JessieS , Welcome to PF !

Are you given any numerical values, particularly any for Ex and Ey ?
 
  • #3
SammyS said:
Hello JessieS , Welcome to PF !

Are you given any numerical values, particularly any for Ex and Ey ?

Thank you!

And no I am not. I am supposed to just use Ex and Ey as variables.
 
  • #4
JessieS said:
Thank you!

And no I am not. I am supposed to just use Ex and Ey as variables.
OK.

You are on the right track.

First, at least one error. What is the distance from q1 to A and q2 to A. The square of each of those distances is 2a2, not 4a2 .

I suggest that you keep Ex and Ey separate, rather than lumping them together into one big vector expression.

You have that Ex = C⋅(q1 - q2) and Ey = C⋅(q1 + q2) , where the coefficient, C is made up of all that stuff in your equation.
 
  • #5
SammyS said:
OK.

You are on the right track.

First, at least one error. What is the distance from q1 to A and q2 to A. The square of each of those distances is 2a2, not 4a2 .

I suggest that you keep Ex and Ey separate, rather than lumping them together into one big vector expression.

You have that Ex = C⋅(q1 - q2) and Ey = C⋅(q1 + q2) , where the coefficient, C is made up of all that stuff in your equation.
Ok, so could I do this?

Since
Ex = 2/√2*(q1 - q2)*(ke/(2a2))

Ey = 2/√2*(q1 + q2)*(ke/(2a2))

Then
(q1 - q2) = (Ex * a2*√2)/ke
+ (q1 + q2) = (Ey * a2*√2)/ke
--------------------------------
q1 = (a2*√2)/ke * (Ex + Ey)

So then

q2 = (a2*√2)/ke * (Ey - Ex)

Is that correct?
 
  • Like
Likes SammyS
  • #6
JessieS said:
Ok, so could I do this?

Since
Ex = 2/√2*(q1 - q2)*(ke/(2a2))

Ey = 2/√2*(q1 + q2)*(ke/(2a2))

Then
(q1 - q2) = (Ex * a2*√2)/ke
+ (q1 + q2) = (Ey * a2*√2)/ke
--------------------------------
q1 = (a2*√2)/ke * (Ex + Ey)

So then

q2 = (a2*√2)/ke * (Ey - Ex)

Is that correct?
Yes. That's it.

Subtracting should give q2.
 
  • #7
SammyS said:
Yes. That's it.

Subtracting should give q2.

Thank you for your help! :smile:
 

Related to Find the unknown charges q1 and q2

1. What is the "Find the unknown charges q1 and q2" problem?

The "Find the unknown charges q1 and q2" problem is a common physics problem that involves determining the values of two unknown electric charges, represented by q1 and q2, based on given information about the charges and their interaction with each other.

2. How do you solve the "Find the unknown charges q1 and q2" problem?

To solve the "Find the unknown charges q1 and q2" problem, you will need to 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 setting up and solving equations based on this law and the given information, you can find the values of q1 and q2.

3. What information is needed to solve the "Find the unknown charges q1 and q2" problem?

To solve the "Find the unknown charges q1 and q2" problem, you will need to know the values of at least two of the following: the force between the charges, the distance between the charges, and the value of one of the charges. Additionally, you will need to know the direction of the force between the charges.

4. Can the "Find the unknown charges q1 and q2" problem have more than one solution?

Yes, in some cases the "Find the unknown charges q1 and q2" problem can have more than one solution. This can happen if the given information is not enough to uniquely determine the values of q1 and q2, or if the equations used to solve for the charges have multiple solutions.

5. How is the "Find the unknown charges q1 and q2" problem related to real-world applications?

The "Find the unknown charges q1 and q2" problem is related to real-world applications in fields such as physics, engineering, and electronics. It can be used to determine the charges on objects, such as particles or conductors, and to understand the behavior of electrical systems.

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