Magnetic flux and flux linkage

A coil rotates at a constant angular speed in a uniform horizontal magnetic field. The diagram shows the instant when the plane of the coil is horizontal.

cross-sectional area of coil = 20 × 10⁻³ m² number of turns in coil = 500 turns magnetic flux density = 50 mT frequency of rotation = 50 Hz

What is the mean induced emf, in V, as the coil rotates through π rad from the position

A circular coil with a radius of 0.10 m has 200 turns. The coil rotates at 50 revolutions per second about an axis which is perpendicular to a uniform magnetic field and in the plane of the coil. The magnetic flux density of the field is 0.20 T.

What is the maximum emf induced in the coil?

Figure 7a shows the front view of a vertical coil mounted on a circular frame.

Figure 7b is a side view showing a section through the frame and coil. A constant direct current in the coil produces magnetic flux represented by the magnetic field lines on this diagram.

Figure 7a Figure 7b

Point Q is at the centre of the coil. A sensor placed at Q detects B_H, the horizontal component of the magnetic flux density. The effect of the Earth’s magnetic field at Q is negligible.

Discuss whether a search coil is a suitable sensor to detect B_H.

B_H is measured at Q with the coil vertical.

The coil is now rotated about Q through 25° as shown in Figure 8. The current in the coil does not change.

A new measurement of B_H is made with the coil fixed in this new position.

Determine the percentage change in B_H produced by this rotation of the coil. Show your working.

Figure 9 shows a protractor being used to measure the angle through which the coil is rotated.

Estimate the percentage uncertainty in this result. Justify your answer.

Figure 10 shows an arrangement of two vertical coils. Four experiments are done using this arrangement.

Coil 1 and coil 2 are identical and have a radius r. The coils are separated by a distance r and have a common axis PR. Q is at the centre of coil 1.

The four different experiments investigate how B_H varies with x, the displacement of the sensor from Q along PR.

In experiment 1, the current in coil 1 is 225 mA and the current in coil 2 is zero.

In experiment 2, the current in coil 1 is zero and the current in coil 2 is 225 mA.

Figure 11 shows the results of experiment 1 and experiment 2.

During experiment 1, B_H is measured with the sensor at Q. The sensor is then moved along PR until the value of B_H is halved. The distance from Q to the sensor is x_0.5

In experiment 3, the current in both coils is 225 mA so that the magnetic fields produced by coil 1 and coil 2 are combined.

The resultant B_H has a constant maximum value in the region between x = and

Deduce, in mT, the value of B_H in this region.

State two characteristics of the magnetic field lines in this region.

In experiment 4, the current in coil 2 is reversed so that the direction of the magnetic field produced by coil 2 is also reversed. The magnitudes of the currents in coil 1 and coil 2 are still 225 mA.

Sketch a graph to show how B_H varies between x = 0 and x = r. The x-axis has been provided for you.

Your graph should include numerical values on your B_H axis that correspond to x = 0 and x = r.

A coil is rotated at frequency f in a uniform magnetic field. The magnetic flux linking the coil is a maximum at time t₁ and the emf induced in the coil is

What is the smallest value of t₁ − t₂?

Figure 7 shows a search coil positioned on the axis of an electromagnet, with the plane of the search coil perpendicular to the axis. A magnetic field is produced by a constant current in the electromagnet. Assume that the magnetic flux density inside the search coil is uniform.

The distance between the search coil and the end of the electromagnet is x. Figure 8 shows how the magnetic flux density B of the field varies with x.

The search coil has 200 turns and a cross-sectional area of 3.5 × 10⁻⁵ m².

The search coil is placed at x = 0.070 m.

Show that the magnetic flux linkage through the search coil is about 5 × 10⁻⁴ Wb.

The search coil is now moved at a constant speed of 0.80 m s⁻¹ along the axis so that

x is increasing. An emf is induced across the terminals of the search coil.

Explain what happens to the value of the emf as the search coil moves.

The search coil passes through the position where x = 0.10 m.

Deduce whether the emf can exceed 5 mV for values of x greater than 0.10 m.

The diagram shows a square coil with its plane parallel to a uniform magnetic field.

The coil always remains within the magnetic field. There are four possible changes to the position of the coil:

• moving it to the left

• moving it towards Y

• rotating it about the axis YYˊ

• rotating it about an axis Z that is at its centre and perpendicular to the plane of the coil.

How many of these changes will result in an induced emf in the coil while the change occurs?

An alternating emf is induced in a coil rotating in a magnetic field.

What is the phase difference between the magnetic flux linkage through the coil and the

A square coil of wire is rotating at a constant angular speed about a horizontal axis. Figure 4 shows the coil at one instant when the normal to the plane of the coil is at 30 ° to a magnetic field.

The area of the coil is 5.0 × 10⁻⁴ m² and the flux density of the uniform magnetic field

The maximum flux linkage of the coil during its rotation is 1.5 × 10⁻³ Wb turns.

Calculate the number of turns in the coil.

Calculate the flux linkage of the coil at the instant shown in Figure 4.

The coil forms part of an electrical generator. Figure 5 shows the emf generated by the coil.

Calculate the peak value of the emf generated.

Sketch on Figure 6 the variation with time of flux linkage for the same time interval as Figure 5.

State Lenz’s law.

Lenz’s law can be demonstrated using a bar magnet and a coil of wire connected to a sensitive ammeter as shown in Figure 6.

The bar magnet is moved towards the coil and is then brought to a halt.

State how the reading on the ammeter changes during this process.

During the demonstration an induced current is detected by the ammeter. The induced current is in the direction E to F.

Explain how this demonstrates Lenz’s law.

Figure 7 shows an arrangement for investigating induced emf.

As shown, the uniform vertical magnetic field is confined to the gap between the poles of the magnet. The plane of the square coil is horizontal and is made of conducting wire. The coil consists of a single turn and is attached by flexible wire to an oscilloscope.

The oscilloscope gives a reading of 2.9 10^–4 V when the coil is moved at uniform speed from position G outside the field to position H inside the field, as shown in Figure 8.

Length of side of square coil = 32 mm

Magnetic flux density of uniform magnetic field = 0.38 T

Calculate the time taken to move the coil from position G to position H.

The square coil is rotated through 360 at a constant angular speed about the horizontal axis shown in Figure 9.

Calculate the angular speed of the coil when the maximum reading on the oscilloscope is 5.1 mV

Initially the plane of the coil is perpendicular to the magnetic field lines as shown in Figure X.

The coil is rotated about a vertical axis by 90° in a time of 0.20 s so that its plane becomes parallel to the field lines as shown in Figure Y. Assume that the rate of change of flux linkage remains constant.

What is the emf induced in the coil?