# Deriving an Expression for an Electric Field along the Z axis

• Cactus
In summary, the field is discontinuous at the negative charge and tends to positive infinity as you approach it from below, and to negative infinity as you approach it from above. This is because the positive direction along the z-axis is defined as "up" and the negative direction is defined as "down". Approaching the charge from below causes the field to climb to infinity, while approaching from above causes the field to decrease to negative infinity. It is important to note that the coordinate system used can affect the results, as seen when comparing results from different coordinate systems.
Cactus
Homework Statement
Hey, so I've been given this advanced question as part of my physics assignment, and I've been having trouble trying to solve it, so far, I've found multiple answers that all contradict eachother and all of which don't seem right so I'm struggling to find the correct solution. I've attached my current solution below but I still feel this is wrong as the graph doesn't match what I'd expect to happen

The question is as follows:
Derive an expression for the electric field along the vertical line that passes through the negativecharge. How many times does the electric field strength pass through zero? For each such zeropoint of the field, what would happen if a positive test charge was released from rest near to(but not directly on top of) the point where the field is zero?

The question refers to the charge setup below, where one I believe would intuitively expect to find two zero points (One below all the charges, and one above all the charges).
Relevant Equations
Coulombs Law

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Your answer looks correct. The field is discontinuous at the negative charge; it tends to positive infinity as you approach the negative charge from below, and negative infinity as you approach it from above. So you follow the black curve for z<d, and the red curve for z>d.

Cactus
mjc123 said:
Your answer looks correct. The field is discontinuous at the negative charge; it tends to positive infinity as you approach the negative charge from below, and negative infinity as you approach it from above. So you follow the black curve for z<d, and the red curve for z>d.
Yeah that's mostly the part that I was confused with, how it approached positive infinity even though its approaching a negative charge, however in writing this I think I figured it out. It approaches positive infinity because in this case I've described positive to be "up" along the z axis (So as it approaches the negative charge from below the field should climb to infinity, and be positive as it is traveling up the axis). Thus this would also be the opposite for approaching the charge from above as the field is now down which is negative?

Edit: Also i forgot to say but thanks for pointing this out, I had a friend who also tried the question but set his coord axis on the negative charge rather than in between the positive charges. That confused me at first but plotting his and my graphs together we find we have the exact same graphs except shifted by a value of d, which makes sense cause our coord system starts a distance of d away from each other. But, yeah, thanks for pointing that out cause I was going crazy trying to figure out why my formula wasn't working and why I kept getting the same formula and it turns out it was all because I was misreading the graph.

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## 1. What is the purpose of deriving an expression for the electric field along the Z axis?

The purpose of deriving this expression is to understand the strength and direction of the electric field at any point along the Z axis. It allows us to calculate the force experienced by a charged particle in this region.

## 2. How is the electric field along the Z axis related to the distance from the source of the electric field?

The electric field along the Z axis is inversely proportional to the distance from the source of the field. This means that as the distance increases, the electric field decreases.

## 3. What is the mathematical formula for the electric field along the Z axis?

The mathematical formula for the electric field along the Z axis is E(z) = (kQ)/z^2, where k is the Coulomb's constant, Q is the source charge, and z is the distance from the source charge to the point of interest.

## 4. How does the electric field along the Z axis change if the source charge is doubled?

If the source charge is doubled, the electric field along the Z axis will also double. This is because the electric field is directly proportional to the source charge.

## 5. Can this expression for the electric field along the Z axis be applied to any type of charge distribution?

No, this expression is specifically derived for a point charge. For other types of charge distributions, the expression may differ and would need to be derived separately.

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