A coil is placed in a uniform magnetic field. If the area of the coil is doubled while the magnetic field strength and orientation remain unchanged, how will the magnetic flux through the coil be affected assuming the initial magnetic flux is a non-zero finite value?
The magnetic flux will double
Magnetic flux (Φ) measures the total magnetic field passing through a surface. It depends on three things — the field strength, the area the field passes through, and the orientation of that area relative to the field:
Φ = B · A · cos θ
- B = magnetic flux density / field strength (here unchanged)
- A = area of the coil
- θ = angle between the field and the normal to the coil's plane (orientation unchanged)
Since B and θ are both held fixed, flux is directly proportional to the area. Doubling the area therefore doubles the number of field lines threading the coil:
Φnew = B · (2A) · cos θ = 2 · (B · A · cos θ) = 2Φ
So the magnetic flux doubles.
It cannot remain the same, because area is an active factor in the flux equation and it has changed. It does not halve — flux rises with area, it does not fall. And it does not become four times, since area appears to the first power, not squared; a fourfold increase would need the area to be quadrupled (or the flux to depend on A2), neither of which is the case here.
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