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.
8.2x10-11
Check ur answer
If I am not wrong, the answer is 9.09E-9
To determine the magnitude of the magnetic field required for no electric field to be created inside the conducting cylinder, we can make use of the induced electric field equation:
E = -Bωr
where E is the induced electric field, B is the magnetic field, ω is the angular speed, and r is the distance from the center of the cylinder.
In order for no electric field to be created inside the conductor, the induced electric field must be zero. This means that the following condition must be met:
Bωr = 0
Since ω is given as 1600 rad/s, we can rewrite the equation as:
Br = 0
From this equation, we can conclude that either B or r must be zero for the induced electric field to be zero. Since we are looking for a non-zero value for the magnitude of the magnetic field, it means that the distance from the center of the cylinder, r, must be zero.
This implies that the entire volume of the conductor is filled with electrons, and the electrons are uniformly distributed. Therefore, the magnitude of the magnetic field required for no electric field to be created inside the conductor is infinity.
In summary, if no electric field is created inside the conductor, it implies that the entire volume of the conductor is filled with electrons and the magnitude of the magnetic field required is infinite.