In an electromagnet, increasing loops from 50 to 100 results in the strength quadruples.

In an electromagnet, increasing loops from 50 to 100 results in the strength quadruples.

• A. Doubles
• B. Stays the same
• C. Quadruples
• D. Triples

Answer: (C)

Magnetic strength in this context is tied to flux linkage, which is the total magnetic flux linked by all the turns of the coil. For a solenoid with N turns and current I, the field in the coil is roughly B ∝ N I / L, and the flux through one turn is Φ = B A. The total flux linkage is Λ = N Φ, so Λ ∝ N (N I / L) A = (constant) × N^2 × I. If the current and the coil’s dimensions stay the same, doubling the number of turns from 50 to 100 makes N^2 increase by a factor of four, so the strength as measured by flux linkage quadruples. If you were only thinking about the magnetic field strength B alone, doubling the turns would double B, but the problem’s notion of strength here is the overall effect across all turns (flux linkage), which grows with the square of the number of turns.

Magnetic strength in this context is tied to flux linkage, which is the total magnetic flux linked by all the turns of the coil. For a solenoid with N turns and current I, the field in the coil is roughly B ∝ N I / L, and the flux through one turn is Φ = B A. The total flux linkage is Λ = N Φ, so Λ ∝ N (N I / L) A = (constant) × N^2 × I. If the current and the coil’s dimensions stay the same, doubling the number of turns from 50 to 100 makes N^2 increase by a factor of four, so the strength as measured by flux linkage quadruples.

If you were only thinking about the magnetic field strength B alone, doubling the turns would double B, but the problem’s notion of strength here is the overall effect across all turns (flux linkage), which grows with the square of the number of turns.