Electric Field Proof: Can Point A Have a Higher Field Than Point B?

In summary: Assuming that the distance is ##r##By equaling the magnitude of the electric field at both points, We will have this equation$$ \frac{2}{x^2} = \frac{12}{r^2} +\frac{1}{(r+x)^2} $$The math becomes difficult here, Is there is a way to perhaps simplify the math here? Should I put some random value of r?No, this is not correct. As you go towards the q charge, the field from the other charge goes to a constant value, but the field from the charge you approach still goes to infinity.
  • #1
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I had a thought about electric fields created by charges
Look at this picture:
Ba73rOX.png

Point ##B## is at the half the distance between ##q## and ##2q##. What I am trying to prove/disprove
That there might be actually a point (##A##) near of charge ##2q## that might have an electric field stronger than the electric field at point ##B##

It seems rational that this could happen

Assume that the distance is ##r##

By equaling the magnitude of the electric field at both points, We will have this equation
$$ \frac{2}{x^2} = \frac{12}{r^2} +\frac{1}{(r+x)^2} $$

The math becomes difficult here, Is there is a way to perhaps simplify the math here? Should I put some random value of r?
Useful notes: x should be really smallAnother question here, does the field have the maximum magnitude at the r/2? Is there is a way to prove that too?
 
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  • #2
The field becomes stronger and stronger, tending to infinity, as you approach either charge. Obviously, this means the field is not the strongest at the midway point.
 
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  • #3
Orodruin said:
The field becomes stronger and stronger, tending to infinity, as you approach either charge. Obviously, this means the field is not the strongest at the midway point.
Dummy me, forgot that :/
Now just going to wait for the 1st quiz
 
  • #4
Here's a question using this setup...

Where is the electric field zero?
 
  • #5
Orodruin said:
The field becomes stronger and stronger, tending to infinity, as you approach either charge. Obviously, this means the field is not the strongest at the midway point.
How about finding the point where the Electric field is strongest between for example x m from the right of q to x m from the left of 2q ?
robphy said:
Here's a question using this setup...

Where is the electric field zero?
On the left side of q, Why would you need that?Note: Forgot to say, that I want x to be bigger than a value. I don't want x to be inside the charge because that will prove it wrong.
 
  • #6
Biker said:
How about finding the point where the Electric field is strongest between for example x m from the right of q to x m from the left of 2q ?
The closer to a charge you go, the stronger the field gets.
 
  • #7
Orodruin said:
The closer to a charge you go, the stronger the field gets.
Yea that is pretty much obvious.
So when we get closer to ##-2q## charge its contribution increases and ##q##'s contribution decreases. However the increment of ##-2q## is bigger than the decrements of ##q## so the closer I get to 2q the stronger it gets. If I go to ##q## instead, I should get less values at every point.

P.S I know we could just get really close to q and get the same thing above. But just asking as if we have a range where we can measure the electric field intensity.

How about the first question?
I got a quartic equation when I substituted r with a value and I ended up with complex numbers. Is that normal? and Why can I get a real number answer?
 
  • #8
Biker said:
If I go to qqq instead, I should get less values at every point.
No, this is not correct. As you go towards the q charge, the field from the other charge goes to a constant value, but the field from the charge you approach still goes to infinity.

Regarding your equation for equal field, it is unclear where the 12/r^2 term comes from. Also note that you placed one charge at x=0 and the other at x=-r.
 
  • #9
Orodruin said:
No, this is not correct. As you go towards the q charge, the field from the other charge goes to a constant value, but the field from the charge you approach still goes to infinity.

Regarding your equation for equal field, it is unclear where the 12/r^2 term comes from. Also note that you placed one charge at x=0 and the other at x=-r.
P.S I know we could just get really close to q and get the same thing above. But just asking as if we have a range where we can measure the electric field intensity.

I said that in the thread about 3 times sir :c, I just want to compare it in a range where we don't go to infinity as for example a range from 1 meter of q to 1 meter of -2q.
and I know what you are referring two since the beginning :c

I will write the steps for the equation after a while. Thanks in advance.
 

1. How is electric field strength measured?

The electric field strength is measured in units of volts per meter (V/m). It is a measure of the force that an electric charge experiences in an electric field.

2. Can the electric field strength at point A be higher than at point B?

Yes, it is possible for the electric field strength at point A to be higher than at point B. This can occur if there is a charge or a group of charges located closer to point A than point B, creating a stronger electric field at point A.

3. What factors affect the strength of an electric field?

The strength of an electric field is affected by the amount of charge present, the distance between charges, and the medium in which the charges are located. The strength also depends on the geometry of the charges, as well as the presence of other charges in the vicinity.

4. How can the electric field strength be calculated?

The electric field strength can be calculated using Coulomb's law, which states that the electric field is directly proportional to the amount of charge and inversely proportional to the square of the distance between the charges. It can also be calculated by dividing the force on a test charge by the magnitude of the test charge.

5. Is the electric field constant at all points in space?

No, the electric field is not constant at all points in space. It varies depending on the location and arrangement of charges. In some cases, the electric field may be zero at certain points, while in others it may be very strong. The electric field is also affected by the presence of conductors and insulators in the surrounding space.

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