Question

The induction and radiation fields of an oscillating dipole become approximately equal at a distance ‘R’. The value of ‘R’ is :

1. \(\frac{\lambda }{6}\)
2. \(\frac{\lambda }{4}\)
3. \(\frac{\lambda }{3}\)
4. \(\frac{\lambda }{2}\)

Answer 1

Correct Answer - Option 1 : \(\frac{\lambda }{6}\)

Concept:

Induction field:

• Predominate at the points close to the current element.
• Represents the energy stored in the magnetic field surrounding the current element or conductor.
• This is also called the near field.

Radiation field

• Predominate at the points for away to the current element.
• It is also called for field or distant field.

Analysis:

When the distance from the current element increases:

• Induction field decreases from its peak value
• Radiation field increases from its minimum value
• Certainly, there will come a distance at which both will become equal.

Conclusion:

It is practically found that the distance at which both fields are equal is r = 0.159λ

Where λ is the wavelength.

So approximately it is equal to 1/6 which is approximately λ/6. Hence option (1) is the most appropriate solution.