Flux linkage is defined as which expression?

Flux linkage is defined as which expression?

• A. λ = N Φ
• B. λ = Φ / N
• C. λ = Φ^2 / N
• D. λ = N / Φ

Answer: (A)

Flux linkage tells you how much magnetic flux is linked by all the turns in a coil. If each turn experiences the same magnetic flux Φ, then the total linkage is the flux per turn times the number of turns, giving λ = NΦ. This shows why the quantity scales with both how many turns you have and how much flux threads each turn. In units, Φ is in webers and N is just a count, so λ comes out in webers-turns. This concept also appears in Faraday’s law in the form ε = - dλ/dt; for a coil with uniform flux, that becomes ε = - N dΦ/dt, linking the coil’s induced emf directly to the rate of change of flux through a single turn times the number of turns. Other forms would misrepresent how linkage scales. Dividing by N would imply more turns reduce linkage, and forms like Φ^2/N or N/Φ don’t reflect the straightforward, linear accumulation of flux with each added turn.

Flux linkage tells you how much magnetic flux is linked by all the turns in a coil. If each turn experiences the same magnetic flux Φ, then the total linkage is the flux per turn times the number of turns, giving λ = NΦ. This shows why the quantity scales with both how many turns you have and how much flux threads each turn.

In units, Φ is in webers and N is just a count, so λ comes out in webers-turns. This concept also appears in Faraday’s law in the form ε = - dλ/dt; for a coil with uniform flux, that becomes ε = - N dΦ/dt, linking the coil’s induced emf directly to the rate of change of flux through a single turn times the number of turns.

Other forms would misrepresent how linkage scales. Dividing by N would imply more turns reduce linkage, and forms like Φ^2/N or N/Φ don’t reflect the straightforward, linear accumulation of flux with each added turn.