# Where along line is electric field zero?

• Neliel06
In summary, the conversation discusses finding the point on a line where the electric field is zero between two like charges. The equation E1=E2 is used to find this point, and a quadratic equation is recommended for a more accurate solution. The final solution involves substituting values, distributing, and using the quadratic formula.
Neliel06

## Homework Statement

Two charges of +4microC and +9microC are 30cm apart. Where on the line joining the charges is the electric field zero?

Ep=E1+E2=0
E1=Kq1/x^2
E2=Kq2/(r-x)^2

## The Attempt at a Solution

Since charges are alike, put Ep=E1-E2=0, then E1=E2
Substituted for E1 and E2

He told us to use quadratic since it's more secure, but that requires the (r^2-2rx+x^2) to be set equal to zero, which i cannot figure out how to do

The way I look at it you get something like:

4/x2 = 9/y2

Taking the square root of both sides yields

2/x = 3/y

That looks a little easier to deal with doesn't it?

Never mind, i got it. I plugged in the values for q1 and q2, distributed, subtracted the right from left, then used quadratic. Thanks for your help anyway!

## 1. What does it mean when the electric field is zero at a certain point on a line?

When the electric field is zero at a certain point on a line, it means that there is no net force acting on a charged particle placed at that point. This is because the electric field is a vector quantity that represents the force per unit charge, so a zero electric field means there is no force acting on the charge.

## 2. How is the location of zero electric field along a line determined?

The location of zero electric field along a line can be determined by analyzing the charge distribution and geometry of the line. This can be done by using mathematical equations, such as Gauss's Law, to calculate the electric field at different points along the line. The point where the electric field is calculated to be zero is the location of zero electric field.

## 3. Can the electric field be zero at more than one point along a line?

Yes, the electric field can be zero at more than one point along a line. This can happen if the line has a symmetric charge distribution or if there are multiple point charges with equal magnitudes and opposite signs along the line. In these cases, the electric field will be zero at the points where the forces from each charge cancel out.

## 4. Is there a relationship between the electric field and the distance from the origin on a line?

Yes, there is a relationship between the electric field and the distance from the origin on a line. The electric field is inversely proportional to the distance from the origin, meaning that as the distance increases, the electric field decreases. This relationship is described by Coulomb's Law, which states that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance.

## 5. Can the electric field ever be exactly zero along a line?

It is possible for the electric field to be exactly zero along a line, but it is rare and usually requires a very specific charge distribution. In most cases, the electric field will be very close to zero but not exactly zero. This is because there are always small fluctuations and uncertainties in the charge distribution and measurements. However, for practical purposes, a very small electric field can be considered zero.

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