Question

Name the waves of longest wavelength and highest frequency in the given electromagnetic waves — microwaves, X-rays, radio waves, and \(\gamma\)-rays. What is meant by displacement current?

Hint:

Displacement current helps to explain how electromagnetic waves can propagate through a vacuum. It allows a changing electric field to produce a magnetic field, completing the symmetry of Maxwell's equations.

Answer 1

In the given set of electromagnetic waves — microwaves, X-rays, radio waves, and \(\gamma\)-rays — the following observations are made:
- Longest Wavelength: Radio waves have the longest wavelength among the given electromagnetic waves. The wavelength of radio waves can range from a few millimeters to several kilometers, which is significantly longer compared to the other waves.
- Highest Frequency: \(\gamma\)-rays (gamma rays) have the highest frequency in the given list. Gamma rays have frequencies greater than \(10^{19}\) Hz, much higher than X-rays, microwaves, or radio waves.
Next, the term displacement current refers to a term used in Maxwell's equations to extend the concept of current to situations involving time-varying electric fields. It is defined as: \[ I_{\text{displacement}} = \epsilon_0 \frac{d\Phi_E}{dt} \] Where:
- \(I_{\text{displacement}}\) is the displacement current,
- \(\epsilon_0\) is the permittivity of free space,
- \(\frac{d\Phi_E}{dt}\) is the time rate of change of the electric flux \(\Phi_E\). Displacement current arises in situations like capacitors in an AC circuit where a changing electric field creates a current in the absence of actual charge movement.