A neutral solid conducting cylinder rotates about its axis with angular speed 1600 rad/s. In addition, there is an external magnetic field of induction B directed along the cylinder's axis. What must the magnitude of the magnetic field in Teslas so that no electric field is created inside the conductor?

Hint: The material is originally neutral. If electric fields are created, then what would that imply about the distribution of the electrons in the metal?

To determine the magnitude of the magnetic field in Teslas so that no electric field is created inside the conductor, we need to understand the relationship between magnetic fields and electric fields in a rotating conductor.

When a conducting material rotates in a magnetic field, it experiences a phenomenon called the Faraday's law of electromagnetic induction. According to Faraday's law, a rotating conductor in a magnetic field creates an electric field within the material.

However, in this scenario, we want to ensure that no electric field is created inside the conductor. This implies that the induced electric field should be balanced by an equal and opposite electric field produced by the distribution of electrons in the conducting material.

In a neutral conductor, the electrons are evenly distributed, and their net charge is zero. If an electric field is created inside the conductor, it means that the distribution of electrons is no longer uniform. There would be excess charges in certain regions, leading to a non-zero electric field.

To prevent this from happening, we need to set the magnitude of the external magnetic field to a value that cancels out the induced electric field. This can be achieved by adjusting the strength of the external magnetic field.

So, in this case, to ensure that no electric field is created inside the conductor, the magnitude of the external magnetic field (B) should be such that it exactly cancels out the induced electric field. This implies that the strength of the magnetic field must be high enough to counterbalance the induced electric field and maintain a uniform distribution of electrons.

To determine the specific value of the magnetic field, additional information about the geometry and material properties of the conducting cylinder would be required.