The electrode structure and electric field of the Penning trap are exactly
as described in Sec. 
.
The polarity of the static potential
between the end caps and ring electrode is chosen to induce axial harmonic
oscillation. If no other potential were present, the
axially-confining electrostatic field would induce exponential radial
displacement. Application of a homogeneous, axially-directed
magnetic field, 
, is responsible for radial confinement in
a Penning trap. Since the magnetic force on a particle of charge ne,
, the magnetic force induces rotational motion in the radial plane and has no axial component.