# Where Is the Net Electric Field Zero Between Two Fixed Charges?

• AFRaven
C = 5.5*10^-6 CIn summary, the conversation discusses the problem of two fixed charges, -29.7\muC and +5.5\muC, separated by a distance of 4m. The first part of the problem asks at what point along the line between the charges is the net electric field zero, and the second part asks for the magnitude of the force on a third charge placed at this point. The solution involves using the equation E=kq/d^{2} and graphing to find the point where the net electric field is zero, which is to the left of the positive charge. The magnitude of the force on the third charge can then be calculated
AFRaven

## Homework Statement

Two charges, -29.7$$\mu$$C and +5.5$$\mu$$C, are fixed in place and separated by 4m
(a) At what spot along the line through the charges is the net electric field zero? Locate this spot relative to the position of the positive charge
(b) What would the magnitude of the force on a third charge +48.7$$\mu$$C placed at this spot

## Homework Equations

E=kq/d$$^{2}$$

## The Attempt at a Solution

......+5.5microC...-29.7microC
o_________________o______________o_________
|---------d---------|------4m-------|

After drawing out the problem as shown above, I found out that the net electric field would be zero to the left of the positive charge (-x direction). I then set up my equation as follows:

E= k(5.5*10^-6)/d$$^{2}$$ - k(2.97*10^-7)/(4+d)$$^{2}$$

I graphed this formula and came up with -5.2109 or -3.24575. I entered both numbers into the system as positive and negative and came up with the wrong answer every time. Also, once I solve for "d", how do I go about finding the magnitude of force on the third charge?

29.7microC = 2.97*10^-5 C

I would like to provide the following response to the above content:

The net electric field is determined by the sum of all the electric fields from the individual charges. When the net electric field is zero, it means that the electric field from one charge is equal in magnitude and opposite in direction to the electric field from the other charge. In this case, the net electric field is zero to the left of the positive charge, as correctly identified.

To find the exact spot where the net electric field is zero, we can use the formula E = kq/d^2, where k is the Coulomb's constant, q is the charge, and d is the distance between the charges. We can set up an equation with the electric fields from the two charges and solve for d. However, it is important to note that the distance d in this formula is the distance between the point where the net electric field is zero and the positive charge, not the distance between the two charges. Therefore, the equation should be:

E = kq/d^2 - kq/(4-d)^2

Solving for d, we get d = 1.6m. This means that the spot where the net electric field is zero is 1.6m to the left of the positive charge.

To find the magnitude of the force on a third charge placed at this spot, we can use the formula F = qE, where F is the force, q is the charge, and E is the electric field at that spot. Plugging in the values, we get F = (48.7*10^-6)(5.5*10^6)/1.6^2 = 0.97N. Therefore, the magnitude of the force on the third charge would be 0.97N.

## What is meant by "Net Electric Field Equals Zero"?

"Net Electric Field Equals Zero" means that the sum of all the electric fields at a particular point is equal to zero. This can occur when there are multiple electric fields present, but they cancel each other out due to their direction and magnitude.

## What are the implications of a net electric field equaling zero?

The implications of a net electric field equaling zero include a lack of overall electric force or movement at a particular point. This can occur in situations where there are equal and opposite charges canceling each other out, or in cases where electric fields from different sources counteract each other.

## Under what conditions does the net electric field equal zero?

The net electric field equals zero when there is either no charge present or when the electric fields from different sources cancel each other out. This can also occur in situations where the electric field is constant and uniform, such as in a parallel plate capacitor.

## How is the net electric field calculated?

The net electric field at a particular point is calculated by adding up all the individual electric fields at that point. This can be done by using the equation E = kq/r^2, where E is the electric field, k is a constant, q is the charge, and r is the distance between the charge and the point where the electric field is being calculated.

## What practical applications does the concept of net electric field equaling zero have?

The concept of net electric field equaling zero has practical applications in various fields such as electrical engineering, physics, and chemistry. It is used in the design and functioning of electronic devices, study of electric fields in different materials, and understanding the behavior of charged particles in different environments.

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