Magnetic Vector Potential: Simple Solenoid
What is the magnetic vector potential A for a long solenoid having n turns per unit length?
QUESTIONS
(Score is number right minus number wrong.)
Although Equation (2) is true, Equation (3) cannot be used to calculate the magnetic vector potential because the integral is undefined for an infinitely long solenoid.
True
False
Barring unusual "twisty-turniness" of the source current, the direction of the magnetic vector potential typically follows the direction of the
magnetic field.
current.
perpendicular to the current.
For the solenoid along the z-axis, the direction of the magnetic vector potential can be expected in the direction indicated by
Equation (8a)
Equation (8b)
Equation (8c)
For a circular path symmetric about the z-axis of the solenoid and INSIDE the solenoid, which is true?
Equation (9a)
Equation (9b)
Equation (9c)
Equation (9d)
Equation (9e)
Equation (9f)
For a circular path symmetric about the z-axis of the solenoid and INSIDE the solenoid, which is true? (See Equation (2).)
Equation (10a)
Equation (10b)
Equation (10c)
Equation (10d)
Equation (10e)
Equation (10f)
According to Equation (4), the magnetic vector potential INSIDE the solenoid is given by
Equation (11a)
Equation (11b)
Equation (11c)
Equation (11d)
Equation (11e)
Equation (11f)
OUTSIDE the solenoid, the magnetic vector potential vanishes because the magnetic field vanishes there. (See Equation (5).)
True
False
For a circular path symmetric about the z-axis of the solenoid and OUTSIDE the solenoid, which is true?
Equation (9a)
Equation (9b)
Equation (9c)
Equation (9d)
Equation (9e)
Equation (9f)
For a circular path symmetric about the z-axis of the solenoid and OUTSIDE the solenoid, which is true?
Equation (10a)
Equation (10b)
Equation (10c)
Equation (10d)
Equation (10e)
Equation (10f)
According to Equation (4), the magnetic vector potential OUTSIDE the solenoid is given by
Equation (11a)
Equation (11b)
Equation (11c)
Equation (11d)
Equation (11e)
Equation (11f)
The magnetic vector potential obtained in this way using Stokes' Theorem and the curl of A cannot be used to calculate the magnetic field itself because the vector potential is not uniquely determined until its curl AND divergence are specified.
True
False
Now explicitly use Equation (7). The divergence of the magnetic vector potential vanishes
inside but not outside.
outside but not inside.
both inside and outside.
neither inside nor outside.
Explicitly apply Equation (6). The curl of the magnetic vector potential vanishes
inside but not outside.
outside but not inside.
both inside and outside.
neither inside nor outside.
The curl of A inside and outside the solenoid correctly gives the magnetic field of the solenoid as given in Equation (5).
True
False
EQUATIONS
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