A coil, [tex]L_1[/tex], produces [tex]200 \, \mu \text{Wb}[/tex] of magnetic flux. A nearby coil, [tex]L_2[/tex], is linked with [tex]L_1[/tex] by [tex]50 \, \mu \text{Wb}[/tex] of magnetic flux. What is the coefficient of coupling, [tex]k[/tex], between [tex]L_1[/tex] and [tex]L_2[/tex]?

Question

21-06-2025
Physics

High School

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A coil, [tex]L_1[/tex], produces [tex]200 \, \mu \text{Wb}[/tex] of magnetic flux. A nearby coil, [tex]L_2[/tex], is linked with [tex]L_1[/tex] by [tex]50 \, \mu \text{Wb}[/tex] of magnetic flux. What is the coefficient of coupling, [tex]k[/tex], between [tex]L_1[/tex] and [tex]L_2[/tex]?

Answer :

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shobhnahs shobhnahs · Answer 1 · 2023-10-09T13:06:48-04:00

Final answer:

The coefficient of coupling, k, between two coils when coil L_1 produces 200 μWb of flux and L_2 is linked with 50 μWb of that flux is 0.25.

Explanation:

The student has asked about the coefficient of coupling, k, between two coils. The coefficient of coupling can be calculated using the formula k = Φ_2 / Φ_1 where Φ_1 is the magnetic flux produced by the first coil and Φ_2 is the flux that links the second coil.

In this particular case, coil L_1 produces 200 μWb of magnetic flux, and coil L_2 is linked by 50 μWb of that flux. Applying the formula, the coefficient of coupling k is calculated as k = 50 μWb / 200 μWb = 0.25. Therefore, the coefficient of coupling between L_1 and L_2 is 0.25, which indicates that 25% of the magnetic flux produced by L_1 links with L_2.

It is important to understand that the coefficient of coupling is a measure of how effectively two coils are magnetically coupled together. A coefficient of coupling of 1 would mean perfect coupling, with all the magnetic flux from one coil linking the other. In reality, a value less than 1 is typical, with various factors such as the distance between the coils and their relative orientation affecting the coupling.