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?
Details and assumptions
The specific charge of the electron is e/me=1.76×10^11C/kg
To determine the magnitude of the magnetic field required such that no electric field is created inside the conductor, we need to consider the conditions necessary for the absence of an electric field.
When a conducting cylindrical object rotates, it creates an electric field due to the induction of charges. For the electric field to be absent inside the conductor, the net charge on the conducting cylinder must be equal to zero.
The induced electric field inside a rotating conducting cylinder is given by:
E = ω * B * r
Where:
E is the electric field
ω is the angular speed of rotation in radians per second
B is the magnetic field induction
r is the radial distance from the axis of rotation
To ensure that the electric field is zero inside the conducting cylinder, we need to set the induced electric field equal to zero. Therefore:
0 = ω * B * r
Since the angular speed (ω) and the radial distance (r) are nonzero, the only way to make the electric field zero is to set the magnetic field induction (B) equal to zero. This implies that no external magnetic field is necessary to cancel out the induced electric field.
Hence, the magnitude of the magnetic field required for no electric field to be created inside the conductor is zero Tesla.