Practise › Questions › Magnetic flux and flux linkage
Magnetic flux and flux linkage questions
Before induction can be stated, it needs its own quantity. Flux counts the field threading an area; flux linkage multiplies by the turns of a coil; and one cosine, of the angle to the coil's normal, handles every tilt in between.
18 original questions · 49 marks · the magnetic flux and flux linkage notes · Magnetic fields
Every question here is written for this library rather than taken from a past paper. Write your answer out before opening a mark scheme: the schemes award marks point by point, and the marks are easier to see when you have something of your own to compare against.
State the equation for the magnetic flux through an area whose normal is parallel to the field, and give the unit of magnetic flux.
Mark scheme
Φ = BA, where B is the flux density and A the area perpendicular to the field (1); unit: weber (Wb) (1).A magnetic field of flux density 0.20 T passes normally through an area of 0.05 m2. Calculate the magnetic flux through the area.
Mark scheme
Φ = BA = 0.20 × 0.05 (1)
Φ = 0.01 Wb (1)Define the flux linkage of a coil and state its unit.
Mark scheme
The product of the magnetic flux through the coil and the number of turns, NΦ (1); unit: weber-turns (1).A circular loop of wire of diameter 8.0 cm lies with its plane perpendicular to a magnetic field of flux density 0.15 T. Calculate the magnetic flux through the loop.
Mark scheme
A = πr2 = π × 0.0402 = 5.0 × 10−3 m2 (1)
Φ = BA = 0.15 × 5.0 × 10−3 = 7.5 × 10−4 Wb (1)State the angle between the normal to a coil and a magnetic field at which the flux linkage of the coil is half its maximum value.
Mark scheme
Flux linkage is proportional to cosθ, and cosθ = 0.5 at θ = 60° (1).The number of turns of a coil is doubled, the flux density it sits in is doubled and its area is halved. State and explain the effect on the flux linkage of the coil.
Mark scheme
Flux linkage NΦ = BAN cosθ is proportional to B, A and N (1); the factor is 2 × ½ × 2 = 2, so the flux linkage doubles (1).A coil of 200 turns and area 0.02 m2 is placed with its plane perpendicular to a magnetic field of flux density 0.15 T. Calculate the flux linkage of the coil.
Mark scheme
NΦ = BAN = 0.15 × 0.02 × 200 (1)
NΦ = 0.60 Wb-turns (1)A coil of 100 turns and area 0.01 m2 is placed in a magnetic field of flux density 0.30 T with the normal to its plane at 60° to the field. Calculate the flux linkage of the coil.
Mark scheme
NΦ = BAN cosθ = 0.30 × 0.01 × 100 × cos 60° (1)
NΦ = 0.15 Wb-turns (1)A magnetic flux of 8.0 × 10−3 Wb passes normally through an area of 0.04 m2. Calculate the magnetic flux density.
A coil is rotated in a uniform magnetic field. Describe how the flux linkage varies with the orientation of the coil, and state the orientations that give maximum and zero flux linkage.
A 400-turn coil of area 1.2 × 10−3 m2 is placed in a magnetic field of flux density 0.25 T. The flux linkage of the coil is 0.060 Wb-turns. Calculate the angle between the normal to the coil and the field.
At a certain location the Earth's magnetic field has flux density 49 μT and points at 66° below the horizontal. A 2000-turn coil of area 0.030 m2 lies flat on a horizontal bench. Calculate the flux linkage of the coil.
A 250-turn coil of area 6.0 × 10−4 m2 sits in a magnetic field of flux density 0.32 T with its plane at 35° to the field. Calculate the flux linkage of the coil. Go on to calculate the change in flux linkage when the coil is rotated so that it is face-on to the field.
A coil of 50 turns and area 0.02 m2 is placed in a magnetic field of flux density 0.40 T. Calculate the flux linkage when the normal to the coil is parallel to the field, and state its value when the normal is at 90° to the field.
A coil of 500 turns and area 0.008 m2 lies with its plane perpendicular to a magnetic field. The flux density increases from 0.10 T to 0.30 T. Calculate the change in flux linkage of the coil.
Describe how a search coil can be used to measure the flux density of a magnetic field.
A student must choose a search coil to detect a weak alternating magnetic field. For a given field, the amplitude of the oscilloscope trace is proportional to the peak flux linkage of the coil. Two coils are available.
Coil P: 500 turns, area 1.5 cm2
Coil Q: 2000 turns, area 0.80 cm2
Deduce which coil the student should choose.A student uses a search coil connected to an oscilloscope to investigate how the flux linkage of the coil depends on its orientation in an alternating magnetic field. Describe how the student should carry out the investigation and how the results confirm that the flux linkage is proportional to cosθ, where θ is the angle between the field and the normal to the coil.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
Practise magnetic flux and flux linkage one question at a time
The player marks nothing for you. It shows one question, waits, then shows the scheme so you can mark yourself, and brings a question back sooner when it went badly.