IMO Practice Test — Magnetic Effects of Current and Magnetism
14 Questions • 15 min • Olympiad level
15:00
Question 1 of 14
If both the speed and the magnetic field acting on a circulating charge are doubled, its radius $r=\frac{mv}{qB}$ becomes:
four times
the same
half
double
Explanation: Doubling $v$ doubles $r$, but doubling $B$ halves it, so $r$ is unchanged.
Question 2 of 14
The kinetic energy of a charge moving in a pure magnetic field:
increases
stays constant
decreases
becomes zero
Explanation: The magnetic force is perpendicular to velocity, so it does no work; KE is constant.
Question 3 of 14
Doubling the number of turns per metre of a solenoid (same current) makes its field:
unchanged
double
half
four times
Explanation: $B=\mu_0 n I\propto n$, so it doubles.
Question 4 of 14
Two wires carry equal currents in opposite directions. The force between them is:
attractive
repulsive
zero
rotational
Explanation: Antiparallel currents repel each other.
Question 5 of 14
A cyclotron cannot accelerate electrons effectively mainly because:
electrons are too heavy
the relativistic mass change disturbs resonance
they have no charge
the field is too weak
Explanation: Light electrons reach relativistic speeds quickly, so the period changes and resonance breaks.
Question 6 of 14
The torque on a current loop is zero when its plane is:
parallel to B
perpendicular to B
at 45 degrees
at 30 degrees
Explanation: Torque $\tau=NIAB\sin\theta$ is zero when the normal is along B, i.e. the plane is perpendicular to B.
Question 7 of 14
A short bar magnet is cut into two equal halves perpendicular to its length. Each piece has a magnetic moment of:
the same
half
double
zero
Explanation: Pole strength is unchanged but length halves, so the moment halves.
Question 8 of 14
On the equatorial line the dipole field points:
along the moment
opposite to the moment
perpendicular to it
radially out
Explanation: The equatorial field is antiparallel to the magnetic moment.
Question 9 of 14
At a place where the dip is $45^\circ$, the horizontal and vertical components of the Earth's field are:
equal
$B_V=2B_H$
$B_H=2B_V$
$B_V=0$
Explanation: $\tan I=\frac{B_V}{B_H}=\tan45^\circ=1$, so they are equal.
Question 10 of 14
A diamagnetic rod suspended in a non-uniform field tends to move:
towards the stronger field
towards the weaker field
perpendicular to the field
not at all
Explanation: Diamagnetics are repelled, moving from strong to weak field regions.
Question 11 of 14
Above its Curie temperature, a ferromagnetic material behaves like a:
diamagnet
paramagnet
superconductor
permanent magnet
Explanation: Thermal agitation destroys domain alignment, so it becomes paramagnetic.
Question 12 of 14
For a permanent magnet the material should have high:
conductivity
retentivity and coercivity
low coercivity
susceptibility only
Explanation: High retentivity keeps it magnetised; high coercivity resists demagnetisation.
Question 13 of 14
Halving the radius of a coil (same current and turns) changes the central field by a factor of:
2
1/2
4
1
Explanation: $B=\frac{\mu_0 N I}{2R}\propto1/R$, so halving $R$ doubles $B$.
Question 14 of 14
An electron and a proton enter the same field with the same speed perpendicular to it. The ratio of their path radii $r_e:r_p$ is:
1:1
$m_e:m_p$
$m_p:m_e$
2:1
Explanation: $r=\frac{mv}{qB}$; with equal $v$, $q$ and $B$, $r\propto m$, so $r_e:r_p=m_e:m_p$.