# Finding the position where the electric field is zero

• JohnnyLaws
JohnnyLaws
Homework Statement
Basically, we have two stationary charged particles. The distance between them is 'd.' We know that they have the same charge of 2*10^-6. The objective is to calculate the distance at which the electric field is zero.
Relevant Equations
I think the equation we need is the electric field equation: E = k*q/(r^2), where k = 8.988 x 10^9 Nm^2/C^2, and 'r' is the distance between a point and the charge that is producing the field
This is the outline of the exercise I did on paper.

So basically, my attempt to solve this involved writing the equations according to the reference frame I chose. The origin is the first charge.

I began by putting the equations on paper:
E = 0=> k*q*1/(x^2)+k*q*1/((x+d))^2 = 0, Note that 'x + d' represents the distance between a point and the second charge.
After solving for 'x,' I obtained a strange result. Following that, I began to manipulate the initial condition, and instead of writing the electric field produced by the first charge with a positive sign, I used a minus sign, and I obtained the correct answer: 'x = d/2'

What I don't understand is why this is working, considering that all particles are positively charged. Shouldn't the electric field always be positive when charges have the same sign?

JohnnyLaws said:
What I don't understand is why this is working, considering that all particles are positively charged. Shouldn't the electric field always be positive when charges have the same sign?
The electric fields due to the two charges are equal and opposite at the midpoint between them. The fields cancel out at that point.

MatinSAR and JohnnyLaws
JohnnyLaws said:
Shouldn't the electric field always be positive when charges have the same sign?
Remember that the electric field is a vector. It has magnitude and direction. The magnitude is what is always positive. What is always true about positive charges is the electric field due to them points away from the charges which could be in the positive x-direction or the negative x-direction as you show in your drawing.

MatinSAR and JohnnyLaws

## 1. What is the electric field?

The electric field is a vector field that represents the force exerted per unit charge at any point in space due to the presence of electric charges. It is defined as the force experienced by a positive test charge placed at that point, divided by the magnitude of the test charge.

## 2. How do you determine the position where the electric field is zero between two charges?

To find the position where the electric field is zero between two charges, you need to set the magnitudes of the electric fields due to each charge equal to each other and solve for the distance. For two point charges, this involves using Coulomb's law to express the electric fields and then solving the resulting equation for the position.

## 3. Can the electric field be zero at a point not between the charges?

Yes, the electric field can be zero at a point not between the charges, especially if the charges are of opposite signs or different magnitudes. The position where the electric field is zero can be found by setting the net electric field due to all charges to zero and solving for the coordinates of the point.

## 4. What role does symmetry play in finding the zero electric field position?

Symmetry can greatly simplify the process of finding the position where the electric field is zero. In cases with symmetrical charge distributions, the electric field components along certain axes may cancel out, making it easier to identify the zero field position. For example, in the case of two equal but opposite charges, the zero field position will lie exactly midway between them.

## 5. How do you handle multiple charges when finding the zero electric field position?

When dealing with multiple charges, you need to consider the vector sum of the electric fields due to each charge. This involves calculating the electric field contribution from each charge at a given point and then summing these contributions vectorially. The point where this sum is zero is the position where the electric field is zero. This often requires solving a system of equations.

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