Solving Electric Field with 3 Point Charges: Find q1 & q2

• WeiLoong
In summary, the resultant electric field at point D can be calculated by setting the equations for Ex and Ey equal to zero. By solving for q1 and q2 using trigonometry and the given equations, the magnitudes of q1 and q2 can be expressed in terms of q. The final values obtained are q1 = 8q and q2 = -11.18q.
WeiLoong

Homework Statement

IF the resultant electric field at D due to the three point charges is zero, find the magnitudes of q1 q2 in terms of q
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Electric Field

The Attempt at a Solution

Ex = E(q1) + E(q2)x = k q1 / AB^2 + k q2 cosθ / BD^2
Ey = E(q2)y + E(q) = k q2 sinθ / BD^2 + k q / CD^2
must be
k q2 cosθ / BD^2 = - k q1 / AB^2
k q2 sinθ / BD^2 = - k q / CD^2
then
q1 = q AB^2 / (tanθ CD^2)
AB = CD
tanθ = AB / BC
then
q1 = q BC / AB = 2 q
and
q2 = - q1 BD^2 / (cosθ AB^2)
cosθ= BC / BD
then
q2 = - q1 BD^3 / (BC AB^2) = - q (BD / AB)^3 = -11,2 q

Did i make some mistake here?

WeiLoong said:
Ex = E(q1) + E(q2)x = k q1 / AB^2 + k q2 cosθ / BD^2
I don't think this should be AB here.

The rest looks fine, but you should define the coordinate axes and the angle in some way.

Oopss!

Correction
Ex = E(q1) + E(q2)x = k q1 / AD^2 + k q2 cosθ / BD^2
Ey = E(q2)y + E(q) = k q2 sinθ / BD^2 + k q / CD^2
must be
k q2 cosθ / BD^2 = - k q1 / AD^2 ...(1)
k q2 sinθ / BD^2 = - k q / CD^2 ...(2)
(2)/(1) I got
q1=8q
Did i make some mistake here?

Looks right.

You also need q2.

Yea i am stucked here T_T
Can i just sub 8q into eq(1)?

Sure.

So i got q2 = (-8q/AD^2)(BD^2/cos)
q2=-11.18q am i doing right?

I get the same result.

thanks!

1. How do I solve for the electric field with 3 point charges?

To solve for the electric field with 3 point charges, you will need to use the equation E = kq/r^2, where E is the electric field, k is the Coulomb's constant, q is the charge, and r is the distance between the point charge and the location where you want to find the electric field.

2. What are the steps to finding q1 and q2 in this scenario?

The steps to finding q1 and q2 in this scenario are as follows:
1. Identify the position and charge of each point charge.
2. Determine the distance between the point charges and the location where you want to find the electric field.
3. Use the electric field equation E = kq/r^2 to calculate the electric field for each point charge.
4. Set up and solve a system of equations using the known electric field values and the unknown charges q1 and q2.
5. Solve for q1 and q2 using algebraic methods.

3. What units should be used for the calculations?

The units used for the calculations should be consistent and in the International System of Units (SI). This means that the charges should be in Coulombs (C), the distance in meters (m), and the electric field in Newtons per Coulomb (N/C).

4. Can this method be used for more than 3 point charges?

Yes, this method can be extended to solve for the electric field with any number of point charges. The same equation E = kq/r^2 can be used, but the number of equations to set up will depend on the number of point charges involved.

5. Are there any limitations to solving for electric field with 3 point charges?

There are some limitations to this method, such as:
- It assumes that the point charges are stationary and do not move.
- It only works for point charges, not for continuous distributions of charge.
- It does not take into account any effects of other nearby objects or external fields.
- It assumes that the charges are not too close together, as this may cause inaccuracies in the calculations.

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