Saturday, April 27, 2019

electromagnetism - How would I go about detecting monopoles?



A question needed for a "solid" sci-fi author: How to detect a strong magnetic monopole? (yes, I know no such thing is to be found on Earth).


Think of basic construction details, principles of operation and necessary components of a device capable of detecting/recognizing a macroscopic object emitting magnetic field of equivalent of order ~0.1-10 Tesla near its surface, but with only one pole, reliably distinguishing it from normal (2-pole) magnets, preferably at a distance.


Preferably a robust method, not involving extremely advanced technology. Detect the presence, possibly distance (or field strength) and direction.


I know of SQUIDs, but these concentrate on extreme sensitivity. I'm thinking of something less sensitive but more robust (like, no need for the monopole to fall through the loop) and still able to recognize a monopole against a magnet.


Also, how would such a macroscopic object behave practically? Such a "one-pole magnet" about the size and strength of a refrigerator magnets - how would it behave around ferromagnetics, normal magnets and so on?



Answer



Consider the motion of a magnetic monopole in a completely symmetric Maxwell system, where $$ \nabla\cdot {\vec B}~=~4\pi\rho_{mag}, $$ and $$ \nabla\times{\vec E}~=~4\pi{\vec J}_{mag}~-~\frac{\partial{\vec B}}{\partial t} $$ The first equation is then a Gauss’ law for magnetic monopole charge, and the second is a magnetic current form of the Maxwell-Faraday equation. For the occurrence of a magnetic monopole flying through space this will act as a transient current. The last term on the right hand side is a displacement monopole current in this case. The left hand side will by Stokes’ law $\int\nabla\times{\vec E}\cdot da~=$ $\int{\vec E}\times d{\vec l}$, produce an electric current in a loop. So the right hand side could be measured by the torque this magnetic field induces on an ordinary magnetic dipole. The right hand side measured in a solenoid. If the left hand side and the last right hand side term do not equal each other in the standard form of the Maxwell equation with ${\vec J}_{mag}~=~0$, this would be a signal for the detection of a magnetic monopole.


No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...