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A conducting coil having N turns and cross-sectional area A is kept with its plane perpendicular to a uniform magnetic field B. If the number of turns of the coil is doubled, the magnetic flux linked with the coil becomes ______.

Asked in GSEB Board March 2022 · Flux through a surface

• (1) N²BA
• (2) (NBA)/2
• (3) NBA
• (4) 2NBA

Step-by-step solution

Why the other options are wrong

• (1) The number of turns enters the flux linkage once, as NΦ, not squared. N² belongs to a solenoid's self-inductance, where the turns both produce the field and link it.
• (2) Halving is the opposite of what happens: every added turn links the same flux BA, so doubling the turns doubles the linkage.
• (3) NBA is the flux linkage before the change; it ignores the added turns.

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