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# 9: Magnetic Potential

• Page ID
5472
• 9.1: Introduction to Magnetic Potential
The force on a charge q in a magnetic field is qv×B . This force (the Lorentz force) does not depend only on the position of the particle, but also on its velocity (speed and direction). Thus the force is not conservative. This suggests that perhaps we cannot express the magnetic field merely as the gradient of a scalar potential function – and this is correct; we cannot.
• 9.2: The Magnetic Vector Potential
• 9.3: Long, Straight, Current-carrying Conductor
• 9.4: Long Solenoid
• 9.5: Divergence
Like the magnetic field itself, the lines of magnetic vector potential form closed loops (except in the case of the infinitely long straight conducting wire, in which case they are infinitely long straight lines). That is to say A has no sources or sinks, or, in other words, its divergence is everywhere zero.