Finding the point where the net electric field is 0

In summary: You would need to solve for both of those components.That's not the total electric field. There are 3 charges, not just one, and the electric field has both an x and a y component. You would need to solve for both of those components.
  • #1
012983
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Homework Statement



Three charges of equal magnitude q reside at the corners of an equilateral triangle of side length a. The topmost charge is positive while the charges at the bottom left and bottom right of the triangle are negative. If point P is midway between the negative charges, at what distance above point P along the +y axis must a -8q charge must be placed so that any charge located at point P experiences no net electric force? The distance from point P to the positive charge is 9 meters.

Homework Equations



E = (kq)/r^2

The Attempt at a Solution



No clue. I think you would find the the electrical field for one of the points and then, using that, find the x and y components of the magnitude. Then solve for 0 = sqrt{(Ex)^2 - (Ey)^2}... but the "any charge located at point P" is confusing me. Or else I'm not thinking correctly.
 
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  • #2
It just means that the electric field at P has to be 0. So assume that the third charge is a distance "a" from P, calculate the electric field at P, and set the result to 0.
 
  • #3
ideasrule said:
It just means that the electric field at P has to be 0. So assume that the third charge is a distance "a" from P, calculate the electric field at P, and set the result to 0.

If the electric field at P is equal to (-4*ke*q)/(3a^2), where ke = 8.99 * 10^9, do I proceed by plugging in -8q for q and setting equal to 0?

If so, how would I solve for a? a could be any number so long as the numerator is 0.
 
  • #4
012983 said:
If the electric field at P is equal to (-4*ke*q)/(3a^2), where ke = 8.99 * 10^9, do I proceed by plugging in -8q for q and setting equal to 0?

That's not the total electric field. There are 3 charges, not just one, and the electric field has both an x and a y component.
 
  • #5


As a scientist, my response to this content would be as follows:

To find the point where the net electric field is 0, we need to use the principle of superposition to calculate the electric field at point P due to each of the three charges individually, and then add them together. Since the positive charge at the top of the triangle and the negative charges at the bottom are equal in magnitude, they will cancel each other out and result in a net electric field of 0 at point P.

To ensure that any charge located at point P experiences no net electric force, we need to place an -8q charge at a distance above point P along the +y axis. Using the equation E = (kq)/r^2, we can calculate the distance at which this charge must be placed. By setting the net electric field at point P to 0, we can solve for the distance r, which in this case is 9 meters.

Therefore, to find the point where the net electric field is 0, we need to place an -8q charge at a distance of 9 meters above point P along the +y axis. This will result in a net electric field of 0 at point P, ensuring that any charge located at this point experiences no net electric force.
 

FAQ: Finding the point where the net electric field is 0

1. What does it mean to find the point where the net electric field is 0?

The net electric field refers to the overall electric field at a specific point, which is determined by the combination of electric fields from all sources in that area. Finding the point where the net electric field is 0 means locating the spot where the electric field is balanced out and there is no resulting force on a charged particle placed at that point.

2. Why is it important to find the point where the net electric field is 0?

It is important to find the point where the net electric field is 0 because it allows us to understand the behavior of charged particles in a given electric field. This point is also known as the point of equilibrium or the point of zero potential, and it helps in analyzing and designing various electrical systems.

3. How can the point where the net electric field is 0 be calculated?

The point where the net electric field is 0 can be calculated using the principle of superposition, which states that the net electric field at a point is the vector sum of the individual electric fields at that point. This can be mathematically expressed as E = E1 + E2 + E3 + ..., where E represents the net electric field and E1, E2, E3, etc. represent the individual electric fields from different sources.

4. What are the factors that affect the point where the net electric field is 0?

The point where the net electric field is 0 can be affected by several factors, such as the magnitude and direction of the individual electric fields, the distance between the sources and the point of interest, and the charge of the particles creating the electric fields. Any changes in these factors can alter the location of the point where the net electric field is 0.

5. Can the point where the net electric field is 0 exist in real-life scenarios?

Yes, the point where the net electric field is 0 can exist in real-life scenarios. For example, in a parallel plate capacitor, the electric field is zero at the midpoint between the two plates. In a dipole, the electric field is zero along the axis passing through the two charges. These are just a few examples, and there are many other situations where the point where the net electric field is 0 exists.

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