Question E9H10:
How can the output voltage of a multiple-turn receiving loop antenna be increased?  

Choices:  
A: By reducing the permeability of the loop shield  
B: By utilizing high impedance wire for the coupling loop  
C: By increasing the number of turns and/or the area enclosed by the loop  
D: All these choices are correct    

Correct Answer is  C: By increasing the number of turns and/or the area enclosed by the loop  

Correct answer: C — By increasing the number of turns and/or the area enclosed by the loop

1) Why C is correct
- A small receiving loop’s open-circuit induced voltage follows Faraday’s law:
  $$v_{\text{ind}} = -N\,\frac{d\Phi}{dt}$$
  With a uniform field, magnetic flux is $\Phi = B\,A\,\cos\theta$, so for a sinusoid $B = B_0\cos\omega t$:
  $$V_{\text{pk}} = N\,A\,\omega\,B_0\,\cos\theta$$
- Therefore, increasing the number of turns $N$ and/or the loop area $A$ directly increases the induced voltage.
- Rules of thumb:
  - Doubling $N$ doubles $V$.
  - Doubling loop diameter quadruples area ($A=\pi r^2$), thus roughly quadrupling $V$ (all else equal).
  - For a given field strength, $V \propto f$ as well.

2) Why the other choices are incorrect
- A: Reducing the permeability of the loop shield
  - Loop shields (usually copper/aluminum) serve as an electrostatic (E-field) shield; their magnetic permeability is already near 1 and not the determinant of induced voltage.
  - If anything, increasing effective permeability (e.g., ferrite core) increases coupling; reducing it would not increase output.
- B: Utilizing high impedance wire for the coupling loop
  - The induced EMF is set by the main loop’s $N$ and $A$, not by the “impedance” of the coupling wire.
  - Coupling loop design is about impedance matching/transformer action; using “high impedance wire” does not intrinsically increase induced voltage and can worsen matching and loss.
- D: All these choices are correct
  - False because A and B are incorrect.

3) Useful formulas and notes
- Faraday’s law for a loop in a uniform field:
  $$V_{\text{rms}} \approx N\,A\,\omega\,B_{\text{rms}}\,\cos\theta$$
- Orientation matters: maximum when the loop plane is perpendicular to the magnetic field ($\cos\theta=1$).
- Practical note: Increasing $N$ also increases inductance and resistance, which can reduce Q; there are diminishing returns. However, for exam purposes, $V$ increases with $N$ and $A$.