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In 1864, James Clerk Maxwell published a theory that included an equation for the speed of electromagnetic waves in a vacuum - AQA - A-Level Physics - Question 2 - 2021 - Paper 7
Question 2
In 1864, James Clerk Maxwell published a theory that included an equation for the speed of electromagnetic waves in a vacuum. Show that Maxwell's theory agrees with... show full transcript
Worked Solution & Example Answer:In 1864, James Clerk Maxwell published a theory that included an equation for the speed of electromagnetic waves in a vacuum - AQA - A-Level Physics - Question 2 - 2021 - Paper 7
Step 1
Show that Maxwell's theory agrees with the accepted value for the speed of light in a vacuum.
Answer
To demonstrate this, we can use the formula for the speed of light given by Maxwell’s equations:
Here, (C) represents the speed of light, (\mu_0) is the permeability of free space, and (\epsilon_0) is the permittivity of free space. According to the standard values:
- (\mu_0 = 4\pi \times 10^{-7} , \text{T m/A})
- (\epsilon_0 = 8.85 \times 10^{-12} , \text{F/m})
Substituting these values into the equation gives us:
This result aligns closely with the accepted value for the speed of light, confirming Maxwell's theory.
Step 2
Explain this experiment with reference to Maxwell's model of electromagnetic waves.
Answer
Maxwell's model indicates that electromagnetic waves consist of oscillating electric (E) and magnetic (B) fields, perpendicular to each other and propagating through space.
In this setup, when T is switched on, an oscillating current flows in the metal rods. This oscillation produces an electric field in T, which varies over time, thus generating a changing magnetic field in the surrounding space.
The changing magnetic field induces an electromotive force (emf) in the conducting loop aerial (D) due to Faraday's law of electromagnetic induction. The varying horizontal field associated with the rods induces an emf in the loop, while the vertical oscillations create additional current in D, thus confirming the existence of electromagnetic waves as proposed by Maxwell.
Step 3
Deduce whether this arrangement can be used to measure the speed of electromagnetic waves suggested by Maxwell’s equation.
Answer
To determine if the setup can measure the speed of electromagnetic waves, we analyze the data provided:
The frequency (f) of the transmitter is given as 75 MHz, or (f = 75 \times 10^6 , \text{Hz}). The distance (d) between the transmitter and the reflector is about 12 m. The wavelength (\lambda) can be calculated using the relationship:
Assuming (v = C) (the speed of light), we can find:
Given that the distance to the reflector (12 m) can accommodate a standing wave condition, the arrangement is suitable for accurately measuring the speed of electromagnetic waves through stationary wave patterns. Therefore, the experiment can indeed be utilized to measure the speed as suggested by Maxwell's equation.