“It doesn't matter how beautiful your theory is, it doesn't matter
how smart you are. If it doesn't agree with experiment, it's wrong.”
– Richard Feynman
Questions involving
magnetic fields are generally simple and interesting. But
questions which appear simple at the first glance may tempt you to commit
mistakes.
Here are a few
multiple choice practice questions (single correct answer type) in this section:
(1) An electron is projected at right angles to a uniform
magnetic field. The quantity that remains constant is
(a) velocity of electron
(b) momentum of electron
(c) kinetic energy of electron
(d) all the above
The velocity and momentum of the electron get
changed since the direction of motion of the electron within the magnetic field
changes continuously. However, the kinetic energy of the electron remains
constant since the magnitudes of the velocity and momentum remain constant.
Therefore, the correct option is (c).
(2) An electron is projected
at right angles to a magnetic field that changes in magnitude with time. The
quantity that remains constant is
(a) kinetic energy of electron
(b) momentum of electron
(c) velocity of electron
(d) none of the above
Since
the magnetic field is changing, an emf is induced. The speed of the electron is
changed and therefore the velocity, momentum and the kinetic energy are
changed. The correct option is (d).
[Note
that the particle accelerator betatron
works on the principle of the production of an accelerating emf due to a
changing magnetic field]
(3) Two very long straight conductors are arranged perpendicular to the
XY plane. Their mid points are at A and B and are at the same distance ‘a’ from the origin (Fig.). Each
conductor carries a current ‘I’ in
the negative z-direction. What is the direction of the resultant magnetic field
at the origin?
(a) along OP
(b) along OQ
(c) along OR
(d) along OS
The
magnetic field produced at the origin O by the current in the conductor located
at A is directed along OY.
[Note that
the current is directed normally into the plane of the figure. You may use
Maxwell’s cork screw rule or the right hand palm rule to obtain the direction
of the magnetic field].
The
magnetic field produced at the origin O by the current in the conductor located
at B is directed along OX’. Since the magnetic fields produced at O by the two
conductors are of the same magnitude, the resultant magnetic field at O is
equally inclined to OY and OX’ and is directed along OP.
4) In question No. (3) the magnitude of the resultant magnetic flux
density at the origin O is
(a) μ0 I/2πa
(b) (√2) μ0 I/2πa
(c) μ0 I/πa
(d) 2 μ0 I/πa
The
magnetic flux density at distance a
from a long conductor carrying current I
is μ0 I/2πa. Therefore, the resultant magnetic
flux density at the origin O due to the two flux densities directed along OY
and OX’ which are at right angles is √[( μ0
I/2πa)2 + ( μ0 I/2πa)2]= (√2)
μ0 I/2πa, as given in option (b).
(5) A bar magnet placed in a non-uniform magnetic field will experience
(a) a torque, but no net force
(b) a net force, but no torque
(c) neither a net force nor a torque
(d) a net force as well as a torque
If a bar magnet is located in a uniform magnetic
field, the poles of the magnet will experience forces of equal magnitude, but
of opposite direction. The net force
acting on the magnet will therefore be zero. But the two equal and opposite
forces will produce a torque which will try to rotate the bar magnet. If the
magnetic field is non-uniform, the forces acting on the poles of the magnet
will be of unequal magnitude so that in addition to a torque, there will be a
net force on the magnet [Option (d)].
