# Moving charge to define magnetic field

1. Why charged particle has to be in motion to define magnetic field?
2. Will magnetic force exert any force on a static charge? (as in the static test charge in electric field)
3. A line from my book reads-
"If a magnetic monopole (individual magnetic charge) were available, we could define magnetic field B in a similar way as electric field."
What would be similar to magnetic field and electric field if individual magnetic charges actually existed?
• Number $2$ is ambiguous - at best, it's implied by $3$. But I vote for the @danielunderwood comment. Commented Nov 16, 2019 at 8:51

1 - A particle doesn't have to be in motion to define a magnetic field. A stationary particle will just create a null magnetic field (see Biot-Savart law).

2 - No. See Lorentz's force $$\vec{F} = q\vec{v}\times\vec{B} = 0$$ if $$v=0$$.

3 - A magnetic monopole would just behave as a source of magnetic fields. In this sense, two stationary magnetic monopoles would exert a force on each other just as two electric charges exert a force on each other (just the force constant would be different). Furthermore, a moving magnetic charge would generate an electric field, just as a moving electric charge generates a magnetic field.

1. Because of the answer to 2.
2. No. This is what distinguishes a magnetic field from an electric field. In an electric field a charge experiences a force (proportional to its charge), whether it's stationary or moving. In a magnetic field a charge experiences a force only if it's moving.

Why is it useful to make the distinction? A simple-minded answer is that a magnet exerts a force on a charge moving near it (making it change its direction of motion) but not on a stationary charge. The dome of a working Van Der Graaff generator exerts forces on both stationary and moving charges.

1. Up until sixty years or so ago, most physicists did define magnetic field strength in terms of the forces on a magnetic pole. The pole was sometimes approximately realised in practice as one pole of a ball-ended magnet. [The magnetic field from a single pole obeys an inverse square law, like an electric field from a point charge (but, if you're using a ball-ended magnet – and there's no alternative in practice! – the law doesn't hold inside the magnet itself!)]

Unlike a moving charge, a magnetic monopole would experience a velocity-independent force in the same direction as the magnetic field it is in, just as a charge experiences a velocity-independent force in the same direction as the electric field it is in. That's the similarity of definition that would be made possible if magnetic monopoles existed.