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Net electric field from multiple charges in 1D

In this video David solves an example problem to find the net electric field created by multiple charges at a point in between them. Created by David SantoPietro.

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• does it mean that the magnitude of net electric field created halfway between two charges of same magnitude and charge be always zero?irrespective of distance between them?Then how do they repel?
• Think of it this way. Two people are pushing each other with the same force. If you go and stand in the middle of them you wont have to apply any sort of force to stand. But the guys on the side, who are actually doing all the pushing will have stop themselves from moving backward with their legs. That's why the charges actually repel if no external force is holding the two charges together.
• Isn't electric field a vector quantity? Then how is it possible to add them up using algebraic sum? shouldn't vector sum be used?
• You are right to assume that it is a vector quantity. The reason we are adding them or subtracting them algebraically is that we have already figured out the direction of the vectors before we write them down. Thus we can decide if the vectors have a positive sign (pointing to the right or up if we have decided that these are the positive directions for example) or a negative sign (pointing to the left or down).
• Why is the negative charge pointing to the right? Shouldn't it be pointing left, since negative and positive charges attract?
• You are right that they attract but when talking about Electric Fields, think about them as roads. When dealing with a negative Q, electric fields always point toward the charge and positive Q field always point away from the charge.
• What does one mean by the point that the two same charges are placed in same line and another charge is brought exactly between the charges such that the system is in an equilibrium?
• My understanding of the question would be this...

equilibrium = these three charges have no acceleration. They dont experience a net force. The forces within the system is balanced.

More detail...

Take two positive charges. A distance r between them. They will feel a mutual force of repulsion.

Now place a negative charge half way between them.
Now the negative charge feels two (equal) forces; one from each of the two positive forces.
Each of the positive forces continue to feel the positive (Repulsive) force from the other positive charge. PLUS the attractive force from the negative charge.

[ Hint: Think about what happens to the forces when r is very large and also when very small]

So; i think the question is asking this... what must the distance r be (the distance between the positive charges) so that all these forces cancel out? ie the system is in equilibrium

Alternatively, the question may be asking you to find r/2. (the distance from centre to outer charges) but the maths is about the same..

Hope that makes sense

[For a mathematical / visual solution You might try drawing graphs of forces/ distance and total (resultant forces) for each particle]
:-)
• What would happen if both charges were negative? They would both point inward, so do they cancel?
• The same thing would happen as in the case for positively charged particles.
But this time each negative charge's electric field will point inwardly towards itself.Since both charges are put at opposite ends,then each charge's electric field will be opposite with respect to the other,thus counteracting each other's effect on the particle placed halfway between them.
• Is there any other unit or name for newtons per coulombs?
(1 vote)
• N/C is the same as volt/meter. Both measure electric field strength
• is the direction of the electric field created by a negative charge radially outward in the vicinity of another negative charge?
(1 vote)
• Electric field direction is always determined by the direction of the force that would be felt by a small positive charge placed in the field at that spot.
• At , how when the direction is right it is +ve , when left it is -ve ?
(1 vote)
• Great question,
The + sign indicates the field ( at some point ) is pointing to the right.
The - sign indicates the field ( at some point ) is pointing to the left.

This comes in incredibly handy when using mathematics to work out electric field problems. Instead of writing 'the electrical field at this point is pointing to the right'
or 'this electrical field is pointing to the left at this particular point' we can express both statements with one of two symbols.