Finding the distance between 2 charges in electric equilibrium.

[Ram012593]

Homework Statement

Charge A and charge B are 2.2m apart.Charge A is 1.0C, and charge B is 2.0c. Charge C, which is 2.0C, is located between them and is in electrostatic equilibrium. How far from charge A is charge C.

Homework Equations

E = KcQ1Q2/r^2-------Electric force Formula where E = electric force, Kc = 8.99*10^9, r = radius
E=Kq/r^2--------------Electric field formula where q = charge of particle, E = electric field, K = 8.99 * 10^9
EQ = F----------------E = electric field, Q = charge of particle, F = force

The Attempt at a Solution

Not really sure how to start this one so if anyone would help me it would be great thanks much in advanced!

 

[tiny-tim]

Hi Ram012593!

If the distance AC is r, then the distance BC is 2.2 - r.

Show us what you get. ​

 

[Ram012593]

Ok I've tried setting the formulas for the forces equal to each other since its electric equilibrium so the forces must be the same and tried to solve for ra the radius of the first two and I am not sure if i did it incorrectly or i made an algebra mistake it could easily be both as I'm not very good at algebra at the moment if anyone would correct me this would be great thanks much:D. Here is a link to a snapshot i took of what i did so far. If i am doing it correctly which is not likely can someone tell me how I could continue. http://postimg.org/image/q4md6ins1/

 

[tiny-tim]

Hi Ram012593!

… I'm not very good at algebra at the moment …

Yes, your method is fine, but your algebra has let you down …

your 1/r² = 2/(2.2 - r)² is correct ,

but you left out the 4.4r term when you expanded that square!

(btw, why use two letters, ra, or maybe r_a, when one letter will do? )

 

[Nickie]

I would approach this problem by first identifying the key information given: the distance between charge A and B, the charges of each particle, and the fact that charge C is in electrostatic equilibrium.

To find the distance between charge A and C, we can use the electric force formula given, where we know the electric force is zero since charge C is in equilibrium. This means that the force between charge A and C must be equal and opposite to the force between charge B and C.

We can set up the following equation:
Kc(1.0C)(2.0C)/r^2 = Kc(2.0C)(2.0C)/(2.2m-r)^2

Simplifying, we get:
1.0/r^2 = 4.0/(2.2-r)^2

To solve for r, we can take the square root of both sides and rearrange the equation to get:
r = 2.2m - 2.2m/√4.0

This simplifies to:
r = 2.2m - 1.1m

Therefore, charge C is located 1.1m from charge A.

We can also use the electric field formula to verify our answer. Since charge C is in equilibrium, the electric field at its location is also zero. This means that the electric field at charge A and charge B must be equal.

Using the formula E = Kq/r^2, we can set up the following equation:
Kc(1.0C)/r^2 = Kc(2.0C)/(2.2m-r)^2

Simplifying, we get:
1.0/r^2 = 2.0/(2.2-r)^2

Solving for r, we get the same result of 1.1m.

In conclusion, the distance between charge A and C in electric equilibrium is 1.1m. This can be verified using both the electric force and electric field formulas.