How is E field conservative

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In summary, to prove that the electric field is conservative, one can show that the line integral of the vector field is independent of the path and depends only on the end points. This can be done experimentally by placing a closed contour of electric wire in the field and observing if a current flows. If no current flows, the field is conservative, but if current does flow, the field is not conservative.
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Identity
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How can you prove that the electric field is conservative? I've learned about stuff like line integrals but I'm not sure how to prove this particular fact.

Thanks
 
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A conservative vector field has the property that the line integral of the vector field is independent of the path and depends only on the end points. This implies that the line integral of the vector field around a closed path is equal to zero. An equivalent property is that the curl of a conservative vector field is equal to zero. Also, the curl of the gradient of a scalar function is equal to zero. The electric field can be expressed as te gradient of a scalar electric potential.

There are enough different ways hinted at in the above paragraph that I'm sure you can easily prove that the electric field is conservative.
 
  • #3
Just want to point out that only an electrostatic field is conservative. The electric field induced by a changing magnetic field isn't.
 
  • #4
Identity said:
How can you prove that the electric field is conservative? I've learned about stuff like line integrals but I'm not sure how to prove this particular fact.

Thanks

If you want to prove experimentally that some electric field is conservative, you can place a closed contour of electric wire, with an in-line ammeter, in the field. If no current flows regardless of the orientation of the wire, then you are dealing with a conservative field. If current does flow, then for selected orientations there is a non-zero emf around the contour and the field is not conservative.
 

1. What does it mean for an E field to be conservative?

When an electric field is conservative, it means that the work done by the field on a charged particle moving along a closed path is zero. This means that the change in potential energy of the particle is also zero, and the electric field is solely dependent on the starting and ending points of the particle's path.

2. Why is it important for an E field to be conservative?

Having a conservative electric field allows for the easy calculation of work and potential energy. It also ensures that energy is conserved within the system, as the work done by the field is equal to the change in potential energy of the particle.

3. How can you determine if an E field is conservative?

An E field can be determined to be conservative by checking if it satisfies the criteria for conservative fields. This includes having a curl of zero (curl E = 0) and being able to be represented as the gradient of a scalar potential (E = -∇V). If these conditions are met, then the E field is conservative.

4. What happens if an E field is not conservative?

If an E field is not conservative, it means that the work done by the field on a charged particle moving along a closed path is not zero. This leads to a change in potential energy for the particle, and energy is not conserved within the system.

5. Can a non-conservative E field still exist in nature?

Yes, non-conservative E fields can exist in nature, as not all fields are conservative. For example, magnetic fields are not conservative, as work is needed to move a charged particle along a closed path due to the changing magnetic field. However, in most cases, electric fields are conservative and non-conservative fields are only present in specific situations or under certain conditions.

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