Level 1 — RecognitionElectromagnetism

Electromagnetism

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Level 1: Recognition Test

Time limit: 20 minutes Total marks: 30

Section A — Multiple Choice (1 mark each)

Choose the single best answer.

Q1. The SI unit of electric field is: (a) N/C (b) C/N (c) N·C (d) V·m

Q2. Electric charge is quantized. The smallest free charge is: (a) $1.6\times10^{-19}$ C (b) $9\times10^9$ C (c) $6.25\times10^{18}$ C (d) $8.85\times10^{-12}$ C

Q3. Coulomb's law force between two point charges varies with separation $r$ as: (a) $1/r$ (b) $1/r^2$ (c) $1/r^3$ (d) $r^2$

Q4. The electric field inside a uniformly charged conducting sphere (in electrostatic equilibrium) is: (a) uniform and non-zero (b) zero (c) $\propto 1/r^2$ (d) $\propto r$

Q5. The capacitance of a parallel-plate capacitor is given by: (a) $C=\varepsilon_0 A/d$ (b) $C=\varepsilon_0 d/A$ (c) $C=Ad/\varepsilon_0$ (d) $C=\varepsilon_0 Ad$

Q6. Energy stored in a capacitor is: (a) $CV$ (b) $\tfrac12 CV^2$ (c) $\tfrac12 QV^2$ (d) $C^2V$

Q7. For $n$ equal resistors $R$ connected in parallel, the equivalent resistance is: (a) $nR$ (b) $R/n$ (c) $R$ (d) $n/R$

Q8. The magnetic force on a charge is $\vec F = q\vec v\times\vec B$ . If $\vec v \parallel \vec B$ , the force is: (a) maximum (b) $qvB$ (c) zero (d) $qv/B$

Q9. Faraday's law states the induced EMF equals: (a) $+d\Phi/dt$ (b) $-d\Phi/dt$ (c) $\Phi/t$ (d) $-B\,dA$

Q10. The speed of light in vacuum is: (a) $\sqrt{\varepsilon_0\mu_0}$ (b) $1/\sqrt{\varepsilon_0\mu_0}$ (c) $\varepsilon_0\mu_0$ (d) $1/(\varepsilon_0\mu_0)$

Q11. The time constant of an RC circuit is: (a) $R/C$ (b) $C/R$ (c) $RC$ (d) $1/RC$

Q12. Maxwell's addition to Ampère's law introduced the concept of: (a) magnetic monopole (b) displacement current (c) drift velocity (d) polarization

Section B — Matching (1 mark each pair, 5 marks)

Q13. Match each source with its field/quantity dependence far from it (or as stated):

Column A	Column B
(i) Infinite line charge, field $E$	(P) $\propto 1/r^2$
(ii) Point charge, field $E$	(Q) uniform (independent of distance)
(iii) Infinite plane sheet of charge, field $E$	(R) $\propto 1/r$
(iv) Electric dipole, field on axis (far)	(S) $\propto 1/r^3$
(v) Solenoid (ideal), interior field $B$	(T) $\mu_0 n I$ , uniform

Section C — True/False WITH justification (2 marks each: 1 for T/F, 1 for reason)

Q14. Equipotential surfaces are always parallel to the electric field lines. (T/F + justify)

Q15. Inserting a dielectric (constant $\kappa>1$ ) between the plates of an isolated charged capacitor increases its capacitance. (T/F + justify)

Q16. Kirchhoff's current law is a statement of conservation of energy. (T/F + justify)

Q17. Lenz's law is a consequence of conservation of energy. (T/F + justify)

Q18. In a purely LC circuit with no resistance, energy oscillates between the capacitor and inductor without loss. (T/F + justify)

Q19. The Poynting vector $\vec S = \tfrac{1}{\mu_0}\vec E\times\vec B$ points in the direction of energy flow of an EM wave. (T/F + justify)

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1 — (a) N/C. $E=F/q$ , force per unit charge → newton per coulomb (equivalently V/m). [1]

Q2 — (a) $1.6\times10^{-19}$ C. Elementary charge $e$ ; all free charge is $q=ne$ . [1]

Q3 — (b) $1/r^2$ . $F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}$ — inverse-square. [1]

Q4 — (b) zero. Excess charge resides on the surface; enclosed charge = 0 → by Gauss's law $E=0$ inside. [1]

Q5 — (a) $C=\varepsilon_0 A/d$ . Larger area/smaller gap → more capacitance. [1]

Q6 — (b) $\tfrac12 CV^2$ . From $U=\int_0^Q \frac{q}{C}dq = \frac{Q^2}{2C}=\tfrac12CV^2$ . [1]

Q7 — (b) $R/n$ . $\frac1{R_{eq}}=\frac{n}{R}$ . [1]

Q8 — (c) zero. $\vec v\times\vec B=0$ when parallel ( $\sin0=0$ ). [1]

Q9 — (b) $-d\Phi/dt$ . Negative sign encodes Lenz's law. [1]

Q10 — (b) $1/\sqrt{\varepsilon_0\mu_0}$ . From Maxwell's wave equation. [1]

Q11 — (c) $RC$ . $\tau=RC$ , units of seconds. [1]

Q12 — (b) displacement current. $\varepsilon_0\, d\Phi_E/dt$ term added to close the loop for time-varying fields. [1]

Section B (Q13, 1 mark per correct pair, 5 marks)

(i) → (R) $E\propto 1/r$ (line charge, $E=\lambda/2\pi\varepsilon_0 r$ )
(ii) → (P) $E\propto 1/r^2$ (point charge)
(iii) → (Q) uniform, $E=\sigma/2\varepsilon_0$ (independent of distance)
(iv) → (S) $E\propto 1/r^3$ (dipole)
(v) → (T) $B=\mu_0 nI$ uniform inside solenoid

[5 × 1]

Q14 — FALSE. [1] Equipotentials are perpendicular to field lines, not parallel: any component of $\vec E$ along the surface would do work moving charge along it, changing potential — contradiction. [1]

Q15 — TRUE. [1] $C=\kappa C_0$ ; dielectric polarization reduces the net field for the same charge, lowering $V$ , so $C=Q/V$ rises by factor $\kappa$ . [1]

Q16 — FALSE. [1] KCL expresses conservation of charge ( $\sum I_{in}=\sum I_{out}$ at a node). KVL is the energy statement. [1]

Q17 — TRUE. [1] The induced current opposes the flux change; if it aided it, energy would grow without a source — violating energy conservation. [1]

Q18 — TRUE. [1] With $R=0$ there is no dissipation; energy shuttles between $\tfrac12 CV^2$ and $\tfrac12 LI^2$ at $\omega=1/\sqrt{LC}$ , the electrical analog of SHM. [1]

Q19 — TRUE. [1] $\vec S=\tfrac1{\mu_0}\vec E\times\vec B$ gives magnitude = power per unit area and direction = propagation/energy-flow direction. [1]

[
  {"claim":"Q6: energy from integral of q/C dq equals Q^2/(2C) = CV^2/2",
   "code":"Q,C,V=symbols('Q C V',positive=True); q=symbols('q'); U=integrate(q/C,(q,0,Q)); result = simplify(U-Q**2/(2*C))==0 and simplify((Q**2/(2*C)).subs(Q,C*V)-C*V**2/2)==0"},
  {"claim":"Q7: n equal R in parallel gives R/n (test n=3)",
   "code":"R=symbols('R',positive=True); n=3; Req=1/(n*(1/R)); result = simplify(Req-R/n)==0"},
  {"claim":"Q10: c=1/sqrt(eps0*mu0) numerically ~3e8 m/s",
   "code":"eps0=8.854e-12; mu0=4*pi*1e-7; c=1/sqrt(eps0*mu0); result = abs(float(c)-2.998e8) < 2e6"},
  {"claim":"Q11: RC has units of time; numeric tau for R=1000,C=1e-6 is 1e-3 s",
   "code":"R=1000; C=1e-6; tau=R*C; result = abs(tau-1e-3) < 1e-9"}
]