IMO Practice Test — Electrostatics
13 Questions • 15 min • Olympiad level
15:00
Question 1 of 13
A charge of $1\ \text{C}$ contains how many electrons (approx.)?
$1.6\times10^{19}$
$6.25\times10^{18}$
$9\times10^{9}$
$6.25\times10^{12}$
Explanation: $n=1/(1.6\times10^{-19})=6.25\times10^{18}$.
Question 2 of 13
Two equal charges repel with force $F$. If each is halved and distance doubled, the new force is:
$F/16$
$F/4$
$F/8$
$F$
Explanation: Charges give factor $\frac14$, distance gives factor $\frac14$; total $F/16$.
Question 3 of 13
On the equatorial line of a dipole the field points:
along $p$
opposite to $p$
perpendicular to $p$
is zero
Explanation: Equatorial field is antiparallel to the dipole moment.
Question 4 of 13
A dipole is in stable equilibrium in a uniform field when $\theta=$
$0^\circ$
$90^\circ$
$180^\circ$
$45^\circ$
Explanation: At $\theta=0$ the dipole aligns with the field — minimum energy, stable.
Question 5 of 13
Flux through a cube enclosing charge $q$ at its centre, through one face, is:
$q/\epsilon_0$
$q/6\epsilon_0$
$q/2\epsilon_0$
$6q/\epsilon_0$
Explanation: Total $q/\epsilon_0$ splits equally over 6 faces: $q/6\epsilon_0$.
Question 6 of 13
A point charge is moved from infinity to distance $r$ from a fixed charge $Q$. The work done equals the:
kinetic energy
potential energy of the pair
flux
capacitance
Explanation: Work done equals the potential energy $U=\frac{1}{4\pi\epsilon_0}\frac{qQ}{r}$.
Question 7 of 13
If $V=10/r$ volts, the field magnitude at $r$ is:
$10/r$
$10/r^2$
$-10/r$
$10r$
Explanation: $E=-dV/dr=10/r^2$.
Question 8 of 13
Equipotential surfaces of a uniform field are:
concentric spheres
parallel planes
coaxial cylinders
ellipsoids
Explanation: A uniform field has planar equipotentials perpendicular to it.
Question 9 of 13
Three $3\ \mu\text{F}$ capacitors in series give:
$9\ \mu\text{F}$
$1\ \mu\text{F}$
$3\ \mu\text{F}$
$6\ \mu\text{F}$
Explanation: $\frac{1}{C_s}=3\times\frac{1}{3}=1$, so $C_s=1\ \mu\text{F}$.
Question 10 of 13
If the voltage on a capacitor is doubled, its stored energy becomes:
double
four times
half
unchanged
Explanation: $U\propto V^2$, so doubling $V$ quadruples $U$.
Question 11 of 13
A parallel-plate capacitor\u2019s plate area is doubled and gap halved. Capacitance becomes:
double
four times
half
unchanged
Explanation: $C\propto A/d$; $\times2$ from $A$ and $\times2$ from $1/d$ gives $\times4$.
Question 12 of 13
Energy density of an electric field is:
$\epsilon_0 E$
$\frac12\epsilon_0 E^2$
$\epsilon_0 E^2$
$\frac12\epsilon_0 E$
Explanation: $u=\frac12\epsilon_0 E^2$.
Question 13 of 13
The net charge of an isolated system is always:
increasing
conserved
zero
quantised away
Explanation: Charge conservation: net charge of an isolated system is constant.