Depth of penetration in induction heating equals

Question

Examoogle · Accepted Answer

Option C: $\sqrt{\frac{1}{Frequency}}$

Explanation & Concepts:
In induction heating, the depth of penetration (often denoted as $\delta$) refers to the depth at which the induced eddy current density falls to $1/e$ (approximately 37%) of its value at the surface. This depth is inversely proportional to the square root of the frequency of the alternating magnetic field.

Working Principle: As an alternating current flows through an induction coil, it produces an alternating magnetic field that penetrates the workpiece. Due to Faraday's law of induction and Lenz's law, eddy currents are generated within the material. The phenomenon of 'skin effect' causes these currents to concentrate near the surface, with the effective depth of penetration determined by the electromagnetic properties of the material and the frequency of the source.

Key Formulas: $\delta = \sqrt{\frac{1}{\pi f \mu \sigma}}$ — where $\delta$ is penetration depth, $f$ is frequency, $\mu$ is permeability, and $\sigma$ is conductivity.

Key Points: Higher frequency results in shallower penetration depth (surface heating).; Lower frequency is used for through-heating of thick components.; The skin effect is the physical mechanism governing this relationship.; Depth of penetration depends on both material properties ($\mu, \sigma$) and supply frequency ($f$).

Advantages: High efficiency due to direct heating of the workpiece.; Precise control over the heated zone and depth.; Rapid heating rates compared to conventional ovens.; Clean and environmentally friendly process.

Disadvantages: High initial setup cost for power supply and coils.; Requires complex impedance matching for efficient operation.; Limited by the geometry of the induction coil.

Applications: Surface hardening of steel gears and shafts.; Induction melting of metals in crucibles.; Brazing and soldering applications.; Shrink fitting of machine components.

Additional Info: The constant of proportionality involves material resistivity and permeability.. Option A and B are incorrect because they imply linear or square relationships, failing to account for the square root dependency in the skin effect formula.

Answer: C is correct — The depth of penetration in induction heating is inversely proportional to the square root of the frequency ($\delta \propto \frac{1}{\sqrt{f}}$).

Exam Tip: Always remember that for eddy current losses and skin effect, frequency is the dominant variable; in high-frequency applications, heat is always concentrated at the surface.

Examoogle · Answer

Option A: Frequency

Examoogle · Answer

Option B: $(Frequency)^2$

Examoogle · Answer

Option D: $\frac{1}{Frequency}$

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)