Cambridge International AS & A Level · 20 · structured
Flux, linkage and the induction laws
Flux, linkage and the induction laws · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 10
- Topics
- 4
- Answer
- Complete
A 300-turn coil has area 4.00×10⁻⁴ m² per turn. A uniform magnetic field initially has magnitude 0.200 T, directed into the page perpendicular to the coil's plane. The field then decreases uniformly to zero in 0.0300 s.
- (a)
Define magnetic flux and calculate the initial flux through one turn. Explain why the coil's area can be used directly here.
3 marks - (b)
Explain flux linkage and calculate its initial value for the coil.
2 marks - (c)
State Faraday's and Lenz's laws, calculate the induced e.m.f. magnitude while the field decreases, and determine the induced conventional-current direction if the coil circuit is closed.
5 marks
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(a)
Define magnetic flux and calculate the initial flux through one turn. Explain why the coil's area can be used directly here.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Magnetic flux is the product of field magnitude and cross-sectional area perpendicular to the field.
- 2
The plane of the coil is perpendicular to B, so its whole area is the perpendicular area.
- 3
Φ=BA=0.200×4.00×10⁻⁴=8.00×10⁻⁵ Wb.
(b)
Explain flux linkage and calculate its initial value for the coil.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Each of 300 turns links the same flux, so total linkage is NΦ.
- 2
NΦ=300×8.00×10⁻⁵=0.0240 Wb-turn; turns are a dimensionless count.
(c)
State Faraday's and Lenz's laws, calculate the induced e.m.f. magnitude while the field decreases, and determine the induced conventional-current direction if the coil circuit is closed.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Faraday's law: induced e.m.f. magnitude is the rate of change of magnetic flux linkage.
- 2
Lenz's law: the induced effect opposes the change causing it.
- 3
|ε|=|Δ(NΦ)|/Δt=0.0240/0.0300=0.800 V.
- 4
The into-page flux is decreasing, so the induced field is into the page to oppose that decrease.
- 5
Clockwise conventional current produces an into-page field; it does not oppose the existing field in this decreasing-field case.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- (a) Magnetic flux is the product of field magnitude and cross-sectional area perpendicular to the field.
- (a) The plane of the coil is perpendicular to B, so its whole area is the perpendicular area.
- (a) Φ=BA=0.200×4.00×10⁻⁴=8.00×10⁻⁵ Wb.
- (b) Each of 300 turns links the same flux, so total linkage is NΦ.
- (b) NΦ=300×8.00×10⁻⁵=0.0240 Wb-turn; turns are a dimensionless count.
- (c) Faraday's law: induced e.m.f. magnitude is the rate of change of magnetic flux linkage.
- (c) Lenz's law: the induced effect opposes the change causing it.
- (c) |ε|=|Δ(NΦ)|/Δt=0.0240/0.0300=0.800 V.
- (c) The into-page flux is decreasing, so the induced field is into the page to oppose that decrease.
- (c) Clockwise conventional current produces an into-page field; it does not oppose the existing field in this decreasing-field case.
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