Oscillating Currents

  • Neil R. SheeleyJr.


Here, we shall consider what happens when the current is repeatedly turned on and off. We begin by ramping the current up linearly during a time Δr ≥ 2 (in units of Rc) and then (after an elapsed time of 2Rc for the bubble to leave the sphere) ramping it down again over an equal time Δr. During the turn-on, a total energy of 3∕2 + (6∕5)( Δr)−2 units is required for the linear ramp: 1 unit for the sphere, 1/2 a unit for the external dipole field, and (6∕5) ( Δr)−2 of a unit for the escaping bubble. During the turn-off, 3∕2 − (6∕5)( Δr)−2 is regained from the field, but (6∕5)( Δr)−2 escapes with the bubble. Thus, in the process of gradually turning the current on, waiting momentarily, and then gradually turning it off again, a total energy of (12∕5)( Δr)−2 is lost to the escaping bubbles.

Supplementary material


  1. Slater JC, Frank NH (1947) Electromagnetism. McGraw-Hill, New York, p 159zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Neil R. SheeleyJr.
    • 1
  1. 1.AlexandriaUSA

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