If the number of turns in a coil is tripled, the value of the magnetic flux linked with the coil:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → is tripled
The magnetic flux linked with a coil is its flux linkage: the flux through one turn added over all N turns. In a given field B, every turn of area A encloses the same flux, so
\( \displaystyle \Phi_{\mathrm{linked}} = NBA\cos\theta \)
Keeping the field, the area and the orientation the same, the linkage is proportional to the number of turns:
\( \displaystyle N \rightarrow 3N \Rightarrow \Phi_{\mathrm{linked}} \rightarrow 3\,NBA\cos\theta \)
So the flux linked with the coil is tripled. This is why a coil with more turns gives a larger induced emf, \( \varepsilon = -N\,d\Phi/dt \), for the same change of field.
Note: The question does not say whether the flux linked with the coil means the total flux linkage or the flux through the area of the coil. If it means the flux through each turn, \( \Phi = BA\cos\theta \) does not depend on the number of turns, and Option (1), “remains unchanged”, is also correct. However, “flux linked with a coil” normally means the flux linkage NΦ, which is proportional to the number of turns and gives the keyed Option (3).