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

In summary, the point of zero electric field on the axis between two equal but opposite charges occurs where the electric fields produced by both charges cancel each other out. This can be determined mathematically by setting the magnitudes of the electric fields from each charge equal, as the direction of the fields will be opposite. The analysis typically involves using Coulomb's law to calculate the electric fields at various points along the axis and identifying the location where their sum equals zero.
  • #1
laser
104
17
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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FAQ: How do we know the point of 0 electric field is on the axis?

How do we determine the point of zero electric field on the axis?

To determine the point of zero electric field on the axis, we analyze the superposition of electric fields from all charges along the axis. By setting the net electric field equation to zero, we solve for the position where the contributions from all charges cancel each other out.

Why is the point of zero electric field always on the axis in symmetrical charge distributions?

In symmetrical charge distributions, the symmetry ensures that the electric field components perpendicular to the axis cancel out, leaving only the components along the axis. This makes the point of zero electric field lie on the axis where the net electric field is zero due to symmetrical cancellation.

Can the point of zero electric field exist off the axis?

For non-symmetrical charge distributions, the point of zero electric field can indeed exist off the axis. However, for symmetrical distributions or those constrained to a line or plane, the zero field point typically lies on the axis due to symmetrical cancellation.

What role does the principle of superposition play in finding the zero electric field point?

The principle of superposition is crucial as it allows us to calculate the net electric field by summing the contributions from all individual charges. By setting this net field to zero, we can solve for the position where these contributions cancel out, indicating the point of zero electric field.

How do boundary conditions affect the location of the zero electric field point on the axis?

Boundary conditions such as the presence of conductive or dielectric materials can alter the electric field distribution. These conditions can shift the point of zero electric field or change its location entirely. However, in free space or simple configurations, the point is typically found using symmetry and superposition principles.

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