A radio transmitter emits an electromagnetic wave whose electric-field vector…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A radio transmitter emits an electromagnetic wave whose electric-field vector oscillates in a horizontal plane. A receiving antenna on a research vessel consists of a straight conducting rod of length ℓ that can be rotated about a vertical axis so that it makes an adjustable angle ϕ with the horizontal direction of the electric field.
The received signal strength is proportional to the magnitude of the electric-field component that acts along the length of the antenna.
Answer each part in sequence, showing clear logic and supporting calculations.
(a) Derive an expression for the induced emf E(ϕ) in the antenna in terms of the maximum electric-field amplitude E0, the rod length ℓ, and the angle ϕ.
(b) If the antenna is initially oriented at ϕ=60∘ relative to the electric-field direction, calculate the ratio of the received signal power to the maximum possible signal power.
(c) The vessel engineers propose installing a second, identical antenna at right angles to the first and electronically combining their outputs. Explain qualitatively and quantitatively how this configuration could recover the full signal power independent of vessel orientation.
(d) Discuss two practical disadvantages of relying solely on mechanical rotation of a single antenna to maintain optimal reception, and suggest how modern communication systems address each disadvantage.