Answer & Solution
Why is the skin effect proportional to the diameter of the conductor?
In skin effect the eddy current causes the electron to be repelled towards the outermost surface of the conductor.
Repelling the electron towards the outer surface of the conductor increase the conductor resistance.
The resistance of a conductor is defined as the resistivity of the conductor multiplied by the length of the conductor, divided by the cross-sectional area.
R=ρl/a ………1
For the cross-sectional area of a conductor:
a = πr2
since the diameter of a conductor is twice its radius, we can write
a = π(D/2)2
Putting the value of a in equation number 1 we get
R=ρlπ/(D/2)2
Thus the resistance of the conductor (R) would increase with a decrease of the diameter (D).
Skin effect is inversely proportional to the skin depth
skin depth = 1/√(πfµσ)
∴ skin effect ∝ √(πfµσ)
Hence skin effect is directly proportional to the (Diameter of the conductor)2
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