How do we know the point of 0 electric field is on the axis?

  • #1
laser
75
10
Homework Statement
E=0
Relevant Equations
Electric field is a vector
In many homework problems I've encountered, they all seem to assume the electric field = 0 point is along the axis of the two charges. Intuitively it kind of makes sense, but I'm looking for a solid justification for it. In other words, why can't it be off the axis of the two charges? When setting up the problem, everyone seems to just assume it is on the axis.

Couldn't find any information about this in the book/online. Thanks!
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  • #2
Draw the electric field at points outside the líne that joins q1 and q2
 
  • #3
The only way to add two vectors to get zero is if they have equal magnitudes and are antiparallel.
 
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  • #4
… and the only places where they are antiparallel is where the two charges and the point of zero field all lie on the same line.
 
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Related to How do we know the point of 0 electric field is on the axis?

1. How do we know the point of 0 electric field is on the axis?

The point of 0 electric field on the axis is determined by the symmetry of the charge distribution. For example, if we have a uniformly charged sphere, the electric field at any point along the axis passing through the center of the sphere will be 0 due to the symmetry of the charge distribution.

2. What is the significance of the point of 0 electric field being on the axis?

The point of 0 electric field being on the axis is significant because it allows us to simplify calculations and make predictions about the behavior of the electric field in a given system. Knowing that the electric field is 0 at a specific point on the axis can help us understand the overall symmetry and behavior of the system.

3. How can we experimentally verify the point of 0 electric field on the axis?

One way to experimentally verify the point of 0 electric field on the axis is by using a test charge and measuring the electric field at different points along the axis. By systematically moving the test charge along the axis and measuring the electric field at each point, we can determine where the electric field is 0 and confirm the location of the point on the axis.

4. Are there any exceptions to the point of 0 electric field being on the axis?

While the point of 0 electric field is typically found on the axis due to symmetry considerations, there can be exceptions depending on the specific charge distribution. In cases where the charge distribution is not symmetric or varies significantly, the point of 0 electric field may not necessarily lie on the axis.

5. How does the concept of the point of 0 electric field on the axis relate to Gauss's Law?

The concept of the point of 0 electric field on the axis is closely related to Gauss's Law, which states that the electric flux through a closed surface is proportional to the total charge enclosed by that surface. By considering the symmetry of the charge distribution and the point of 0 electric field on the axis, we can often apply Gauss's Law to simplify calculations and analyze the electric field in a given system.

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