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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
Step 1
Answer
Maxwell's equation for the speed of electromagnetic waves is given by:
where:
is the speed of light,
is the permeability of free space, and
is the permittivity of free space.
From the data booklet, we know that:
Substituting these values into the formula, we calculate:
Calculating this gives us approximately , which aligns with the accepted value of the speed of light in a vacuum.
Step 2
Answer
In this experiment, the radio wave transmitter T generates an oscillating current, which creates an alternating electric field (E-field) and magnetic field (B-field) perpendicular to each other and to the direction of wave propagation, consistent with Maxwell's model of electromagnetic waves.
The oscillating current in T induces a horizontal electric field that propagates through space. As this E-field varies, it induces a magnetic field around the conductive loop aerial D. The varying magnetic field generates an electromotive force (emf) in the loop aerial.
This implies that electromagnetic waves can transmit energy through space, as the oscillating E-field creates a corresponding B-field, enabling energy transfer between the transmitter and the detector via the space between them.
Step 3
Answer
In the given experimental setup, stationary waves form between the fixed transmitter and the fixed reflector. The distance between them is approximately 12 m and the transmitter frequency is 75 MHz.
The wavelength () can be calculated using:
where and .
Calculating gives us:
Since the distance between the transmitter and the reflector is greater than half of the wavelength (i.e., greater than 2m), this arrangement can indeed be used to measure the speed of electromagnetic waves as suggested by Maxwell's equation.
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