# Explaining induced emf: directions of lorentz force and electrostatic field in two reference frames [closed]

First question, what is the direction of electrostatic field?

Here is the problem: Consider a conductor rod CD moving at a speed v in a magnetic field. The three are in right angles to each other. In reference S, rod does not move with the positive charges contained within it. As B is pointing out of the plane, the Lorentz force is in the direction D to C. Electric field is said to be in the direction C to D. Why are they in opposite directions?

In another reference frame, where the rod moves with the charges.

The charges do not experience Lorentz force. Then, the textbook says 'nevertheless the force directed from D to C acts on the charge q so the electric field is induced in the direction D to C'. Where does this force come out in this reference frame?

How does this situation apply to a square coil where one side of the coil experiences a magnetic field? It is easy to think that the opposite sides have emfs in opposite directions but I am having problems with visualising why it is.

## closed as off-topic by Yashas, Jon Custer, GiorgioP, Rory Alsop, ZeroTheHeroMay 5 at 23:33

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In the first diagram, it appears that the rod is moving to the right with uniform speed $v$ and the magnetic field is pointing into the page. In this case, the magnetic force on a positive charge is towards the top of the page.

Assuming positive charge is free to move inside the rod, the charge will redistribute until there is no longer a net force on the free charge.

This means that the charge will accumulate at one end creating an electric field that produces an electric force that is opposite the magnetic force.

In summary, in this frame, there is a magnetic force due to the motion of the rod and there is an opposing electric force due to the charge distribution within the rod.

In the second diagram, the rod is at rest in this frame so there is no magnetic force on the charge in the rod.

However, the purely magnetic field in the first frame is a mixture of magnetic and electric in this frame since electric and magnetic fields transform between inertial reference frames.

In this frame, there is an external electric field$^1$ directed towards the top of the page and so, there is an electric force on the charge in the rod in the same direction as the magnetic force in the first frame.

As before, the charge will redistribute until there is no longer a net force.

In summary, in this frame, there is an external electric field that produces a force on the charge as well as an opposing electric force due to the charge distribution within the rod.

$^1$ A quick calculation of the magnitude of the electric field in this frame yields $E' = \gamma v B \approx vB$ so the electric force on a charge in this frame is $qvB$, the same as the magnetic force in the first frame.

How does this situation apply to a square coil where one side of the coil experiences a magnetic field?

Please edit your question with more detail or, better, post a new question as a follow up to this one.