Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

284 Aptitude Test Problems in Physics

The velocity of the jumper at the foot will be

21mg sin a
vf = at=
m+ Cb 2 B 2 cost a •

3.54*. The magnetic flux across the surface bounded
by the superconducting loop is constant. Indeed,
AO/At =W, but = IR = 0 (since R = 0),
and hence D = const.
The magnetic flux through the surface bounded
by the loop is the sum of the external magnetic
flux and the flux of the magnetic field produced by
the current I passing through the loop. Therefore,
the magnetic flux across the loop at any instant is

= a 2 B 0 a 2 az + LI.

Since = Boat at the initial moment (z = 0 and

I = 0), the current I at any other instant will be

determined by the relation

LI= —aza 2 , I =

aza2

L •

The resultant force exerted by the magnetic
field on the current loop is the sum of the forces
acting on the sides of the loop which are parallel
to the y-axis, i.e.
F= 2a I ax I I = a 2 a/

and is directed along the z-axis.
Therefore, the equation of motion for the loop
has the form

mg—a 4 a 2 z

mz= — mg+ a (^2) aI =

__

L •

This equation is similar to the equation of vibra-
tions of a body of mass m suspended on a spring
of rigidity k = a 4 a 2 /L:

• •
  mz = —mg — kz.

This analogy shows that the loop will perform har-
monic oscillations along the z-axis near the equi-