Electric Field Direction: Are We Assuming a Universal Positive Frame?

[justacuriouskid]

TL;DR

Do electric field directions assume a positively charged background? Just wondering if field lines are defined based on this assumption.

Hey! I'm a high school student trying to understand electric fields at a deeper, more conceptual level. I had a random thought I wanted to share to get your views on it.
So far, I've learnt that electric field lines of a positive charge run outward and that of a negative charge run inward.

But here's where I wondered:
Is this direction based on a positively charged background?
How can we assume a "Default" direction for a field line? What if the surroundings weren't always neutral or positive? Would that affect how we even define field lines?
Thanks in advance!

 

[Baluncore]

Welcome to PF.
Voltage is a potential difference. There must always be a zero reference voltage somewhere, often called ground.

 

[weirdoguy]

Is this direction based on a positively charged background?

It's based on a convention that test charge is positive, and definition of $\vec{E}=\frac{\vec{F}}{q}$. For positive source it is outwards, and so are field lines, since their direction is the direction of electric field vector, per definition. It could be the other way around, if people agreed to use negative test charges.

Also I don't know what you mean by "charged background" since there is no background in the definition

EDIT: I wonder if electric field vector was defined at your school already, because it's crucial in all of this.

 

[justacuriouskid]

Welcome to PF.
Voltage is a potential difference. There must always be a zero reference voltage somewhere, often called ground.

Yeah. So if voltage is relative to a reference, why not electric field lines?

 

[Ibix]

Yeah. So if voltage is relative to a reference, why can't electric field lines?

Because they point up or down the potential gradient, and which direction it's sloping is independent of where you call zero. The convention is around where you put the arrowhead - pointing towards more negative or more positive - but the direction of the lines is not arbitrary.

 

[Baluncore]

So if voltage is relative to a reference, why can't electric field lines?

Why can't electric field lines what?

If not specified, it is probably assumed that there is a potential of zero, at a distance of infinity in all directions.

 

[weirdoguy]

We are talking about field lines, or about voltage? I see no voltage in OP.

 

[Baluncore]

We are talking about field lines, or about voltage? I see no voltage in OP.

The failure of the OP to mention potential difference, or voltage, should not cripple the response.
The electric field lines flow down the potential gradient. The lines that radiate from a positive charge will end at a lower potential, they may converge again at a negative charge, or they might spread out to a zero potential ground.

 

[justacuriouskid]

So, like the direction of the electric field lines is defined as their direction in a neutrally or positively charged surrounding, right? In that case, when we consider a negatively charged surrounding, the definition doesn't always stand true, right?

 

[weirdoguy]

The failure of the OP to mention potential difference, or voltage, should not cripple the response.
The electric field lines flow down the potential gradient

Well, yes, but field lines are integral curves of electric field, and in non-static situations one does not have potential, so for me thinking in terms of E vector is kind of superior. But I know, it's high school level... Anyways, it all boils down to the fact that test charge is positive.

 

[weirdoguy]

So, like the direction of the electric field lines is defined as their direction in a neutrally or positively charged surrounding, right?

No, direction of electric field lines is the direction of the force that would act on a positive charge at the point you are considering.

 

[justacuriouskid]

What will happen to electric field lines in a nonlinear field?

 

[Baluncore]

So, like the direction of the electric field lines is defined as their direction in a neutrally or positively charged surrounding, right? In that case, when we consider a negatively charged surrounding, the definition doesn't always stand true, right?

No. The gradient from positive to ground, or to a negative environment, is still downhill. The downwards gradient, in volts per metre, will be steeper, in a more negative environment.

 

[Baluncore]

What will happen to electric field lines in a nonlinear field?

What do you mean by a non-linear field?

 

[Ibix]

What will happen to electric field lines in a nonlinear field?

Let's just take a step back before you throw in new terms that probably don't mean what you think they mean.

When you talk about a "background", are you imagining something like a sea of electrons and one small region with slightly fewer electrons? So there is everywhere a negative charge but one small region is slightly less negative? And then you are asking about the field in this sea around this small region that is still negatively charged, just slightly less so than its surroundings?

 

[justacuriouskid]

Yeah, here is where I’m confused. We learnt that the direction of the electric field lines depends on the direction of the potential gradient. Now if I consider environment, which is not in vacuum or a neutral surroundings what will happen?
Consider space, an astrophysical environment where it’s filled with plasma, which is just a non-linear environment. What happens?

 

[Ibix]

which is just a non-linear environment.

Not in any relevant sense, no. It's just a sea of positively and negatively charged particles. You can add the fields of each one together, either adding the potentials or adding the force vectors at each point. The field lines inside the plasma will run from positive charges to negative ones, and they'll be really messy and time dependent. That's all.

 

[justacuriouskid]

Not in any relevant sense, no. It's just a sea of positively and negatively charged particles. You can add the fields of each one together, either adding the potentials or adding the force vectors at each point. The field lines inside the plasma will run from positive charges to negative ones, and they'll be really messy and time dependent. That's all.

Yeah, but these force vectors change rapidly because of particle collisions, acceleration, etc., don't they?

 

[weirdoguy]

They do, but the definitions and directions of field lines still work the same. Although, then scalara potential is not enough, and electric field depends on the magnetic vector potential also.

 

[justacuriouskid]

Ok, let me get this straight. I understand that the direction of field lines is gonna always be in the direction of the force. Now, my bigger question is, about the total electric field. So for linear systems, we find the total electric field as the vector sum of the electric fields of the involved charges. But in case of plasma, where force vectors change so quickly, is there a way by which we can actually determine the total electric field?

 

[weirdoguy]

is there a way by which we can actually determine the total electric field?

It's still the sum of electric fields. Non-linear medium does not mean that electrodynamics is not linear - Maxwell equations are always linear.

PS. Is that Ariana Grande in your avatar?