# Another way of stating Gauss' law?

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• rudransh verma
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When you place two positive charges near each other what pattern of field lines form. Both the field lines from the charges get bent in front of each other. The field lines from one charge does not cross through the other charge. It gets deviated in the way.
No it is the resultant field that has bended field lines. The constituents of the resultant field each remain as if they were the only field present in space.

I suggest you read about the superposition principle, maybe your book has a section on it, if not try wikipedia
https://en.wikipedia.org/wiki/Superposition_principle

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No it is the resultant field that has bended field lines. The constituents of the resultant field each remain as if they were the only field present in space.
Here in this figure I can see there are two types of lines. One from one charge and another from other charge. If I take one charge away then the field lines will straighten up. There is no resultant field of lines. We only see resultant‘s effect when we place a test charge. That is what I was trying to say before. There are two constituent fields bent like that but no third resultant field.

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No I insist those field lines are the field lines of the resultant field.

vanhees71
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Maybe now I got it. The new field has no lines of force. It’s just an effect of two fields due to charge q and Q, Q being outside the surface. There is no lines of force actually penetrating the surface from this new field. The only field of lines are from q andQ.There is no source charge inside the surface. Only source are q and Q combined. And so zero flux due to this field. And so the only fluxes are x, -y, +y which comes x as net flux. So Q charge is useless in gauss law.
Any field has field lines. If there are no sources inside a closed surface as many field lines enter this surface as leave it and thus the total flux through the closed surface is 0. In electrostatics the charges are sinks and sources of the field lines.

The great thing is that you only need to understand this for a point charge, i.e., the Coulomb fields. All other fields then can be calculated by superposition:
$$\vec{E}(\vec{x})=\int_{\mathbb{R}^3} \mathrm{d}^3 x' \frac{\rho(\vec{x}')(\vec{x}-\vec{x}')}{4 \pi \epsilon_0 |\vec{x}-\vec{x}'|^3}.$$

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No I insist those field lines are the field lines of the resultant field.
I mean there are two fields physically. There is no resultant field physically. Its only an effect.

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No I don't agree with this. Of course there is the resultant field physically. You said it yourself many times, if we put a test charge it will move in the direction of the resultant field.

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No I don't agree with this. Of course there is the resultant field physically. You said it yourself many times, if we put a test charge it will move in the direction of the resultant field.
Yes, it will. Let me explain. If suppose I place a charge it will setup its field all straight up. Now place a test charge. It will start to move in a straight line. Now as it moves a little bit place a second charge in vicinity. What will happen. The path of test charge will deviate. Meaning now the second charge’s field has bent the field of first one. There is no resultant field here. Only an effect.

Suppose there are two forces applied to a body one is horizontal and one is making theta angle with it. Now the body doesn’t move in horizontal direction but in a direction between the two force’s direction. That doesn’t mean there is a resultant force physically. There are only two forces physically, one is horizontal and other making theta angle with it. It’s because there are two forces in two directions that the body now moves in new direction. We say that body moves in the direction of resultant force.

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I sense there is some sort of weird misunderstanding in your mind, regarding what exactly a resultant field is but I can't figure out what it is.
I 'll just repeat myself, the resultant field is physical. I got no clue what you mean by "There is no resultant field. Only an effect."

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I sense there is some sort of weird misunderstanding in your mind, regarding what exactly a resultant field is but I can't figure out what it is.
I 'll just repeat myself, the resultant field is physical. I got no clue what you mean by "There is no resultant field. Only an effect."
What do you think about force. Is there actually a resultant force?

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What do you think about force. Is there actually a resultant force?
Depends how you see it. It is the force by which you can replace the constituent forces and it will have the same motional effect as the combination of the constituent forces.

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Depends how you see it. It is the force by which you can replace the constituent forces and it will have the same motional effect as the combination of the constituent forces.
Yes, it’s either the constituent forces or a resultant force but not both at one time.

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Yes, it’s either the constituent forces or a resultant force but not both at one time.
yes that's correct.

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yes that's correct.
So in the same way it’s either two fields or one resultant field at a time but not both. Effect will be same in either case. And here it’s two fields whose effect is same as if there were one resultant field.