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I want to ask about the Hall effect. Why is the force by the electric field appearing? I can understand the appearance of the Lorentz force. However, I do not know for what reason the force due to the electric field is generated from there.

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The Lorentz force creates makes for an excess of positive charge at the top (ceiling) of the wire (electrons travel up from the floor to the ceiling of the wire).

At equilibrium:

  1. Lorentz force pushes the current electrons up
  2. The extra charges that have accumulated at the top of the wire (ceiling) push the traveling current charges down.

Such that vertical (up-down) forces are just balanced and current flows horizontally (left-right) without additional acceleration up or down.

Thus for a brief moment, charges will accumulate at the top of the wire due to the Lorentz force.

Afterwards, any additional current will continue feeling the Lorentz force pushing them to go up, but they will also feel the downward force from the charges that had previously accumulated at the top. These would just balance each other and the current will continue flowing horizontally without further digression from horizontal flow.

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