Magnetic flux density

A horizontal wire is perpendicular to a horizontal uniform magnetic field of flux density B. The wire has length L and diameter d. The current in the wire is I.

The magnetic force acting on the wire is equal in magnitude and opposite in direction to the weight of the wire so that the wire is supported.

The wire is replaced with a second wire in the same orientation and position. The second wire is made of the same material and has length and diameter 2d.

What current is required to support the second wire?

This question is about a method to investigate how the force on a conductor varies with flux density and current (required practical activity 10).

Figure 10 shows a copper rod clamped above a horizontal bench.

Figure 10

Describe a method to show that the copper rod is horizontal. Your method must include the use of a metre ruler. You may annotate Figure 10.

Figure 11 shows the copper rod positioned above a digital balance.

Two identical magnets are mounted on a steel yoke with their opposite poles facing each other. The balance is zeroed. The yoke is then placed on the balance so that a horizontal uniform magnetic field is applied perpendicular to the copper rod. The ends of the rod are connected as shown.

When the switch is open, the reading on the balance shows the mass of the yoke and the two magnets. When the switch is closed, the reading on the balance decreases.

Explain, with reference to Figure 11, the direction of the horizontal magnetic field.

The current I in the rod is varied. The balance reading M₁ is recorded for different values of I.

The switch is now opened. Two additional magnets, identical to those used before, are attached to the yoke.

Figure 12 shows how this new arrangement compares with the arrangement in Figure 11.

The balance reading with four magnets attached to the yoke is M₂. With the switch open, M₂ is the mass of the yoke and the four magnets.

The switch is now closed. M₂ is recorded for different values of I.

Figure 13 shows data from both experiments. Values of M₁ and M₂ are plotted using different vertical axes.

It can be shown that

M = kBI + nZ + Y

where

M = balance reading when the current is I B = magnetic flux density of the horizontal uniform magnetic field n = number of magnets attached to the yoke Z = mass, in g, of each magnet Y = mass, in g, of the yoke k is a constant.

Deduce the fundamental base units for k.

Determine Y.

A student sets up the apparatus with the copper rod positioned incorrectly.

Figure 14 shows how the student’s arrangement compares with the correct arrangement.

The student produces a graph of M₁ against I.

Compare the student’s graph with the graph of M₁ against I (the solid line) in Figure 13. Explain your answer.

A wire is at right angles to a uniform magnetic field and carries an electric current. The wire is 150 mm in length.

When the current in the wire is increased by 4.0 A, the force acting on the wire increases

What is the magnetic flux density of the field?

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 horizontal wire of length 0.25 m carrying a current of 3.0 A is perpendicular to a magnetic field. The mass of the wire is 3.0 × 10⁻³ kg and the weight of the wire is supported in equilibrium by the magnetic field.

What is the flux density of the magnetic field?

A short copper rod R is placed on a pair of thick horizontal parallel copper rails. A horizontal magnetic field exists in the direction shown by the dashed arrows. The diagram shows the apparatus when viewed from directly above.

When switch S is closed, R will tend to

The diagram shows a current I in a vertical square coil. The coil can rotate about an axis OO’. The plane of the coil is at right angles to a uniform horizontal magnetic field of flux density B.

Which statement is correct?

The plane of coil PQRS is parallel to a uniform magnetic field.

When a current I is in the coil

A horizontal wire of length 0.50 m and weight 1.0 N is placed in a uniform horizontal magnetic field of flux density 1.5 T directed at 90° to the wire.

What is the current that just supports the wire?

The diagram shows a clockwise current I in a circular coil placed in a uniform magnetic field B with the plane of the coil perpendicular to the magnetic field.

What is the effect on the coil of the interaction between the current and the magnetic field?

This question is about using a digital balance to investigate the force on a wire placed in a magnetic field when there is an electric current in the wire.

A student carries out the procedure shown in Figure 1 and Figure 2. A metre ruler is pivoted at the 1.0 cm mark and a prism is placed on a digital balance. The free end of the ruler is raised and the balance is turned on and then set to zero, as shown in Figure 1.

The ruler is then supported by the prism with the apex of the prism at the 30.0 cm mark as shown in Figure 2. The height of the pivot is adjusted so that the ruler is horizontal.

Deduce the mass of the ruler. State one assumption you make.

The student attaches a uniform wire to the upper edge of the ruler, as shown in Figure 3.

The ends of the wire are connected to terminal blocks P and Q which are fixed firmly to the bench. A power supply and an ammeter are connected between P and Q.

These modifications cause the balance reading to increase slightly.

A horizontal uniform magnetic field is applied, perpendicular to the wire, between the 85 cm and 90 cm marks, as shown in the close-up diagram in Figure 3.

The balance reading M is recorded for increasing values of current I. A graph of these data is shown in Figure 4.

State and explain the direction of the horizontal uniform magnetic field.

It can be shown that B, the magnitude of the magnetic flux density of the horizontal uniform magnetic field, is given by

where change in force acting on the prism per unit current in the wire L = length of the region where the magnetic field cuts through the wire.

Determine B.

The experiment is repeated with the ruler pivoted at the 99.0 cm mark. Nothing else is changed from Figure 3.

This arrangement is shown in Figure 5.

Tick () one box in row 1 and one box in row 2 of Table 1 to identify the effect, if any, on the magnitude of the forces acting on the apparatus as a certain current is passed through the wire.

Tick () one box in row 3 and one box in row 4 of Table 1 to identify the effect, if any, on the graph produced for this modified experiment compared with the graph in Figure 4.

Figure 6 shows the balance being used to measure the forces between two wires. The connections joining these wires to the power supply are not shown.

The pan of the balance moves a negligible amount during use and it supports a straight conducting wire X of horizontal length L. Terminal blocks are used to connect X into the circuit. The weight of these does not affect the balance reading. A second conducting wire Y is firmly supported a distance d above X.

Show, by adding detail to Figure 6, the wire connections that complete the circuit. The currents in X and Y must have the same magnitude and be in the directions indicated.

The vertical force F on wire X due to the magnetic field produced by wire Y is given by

where k is a constant d is the perpendicular distance between X and Y I is the current in the wires and L is the horizontal length of wire X.

A student wants to measure k using the arrangement in Figure 6.

The student is told that the following restrictions must apply:

• L is fixed

• I must not exceed 5.0 A

• the result for k must be obtained using a graphical method

• the experimental procedure must involve only one independent variable.

Explain what the student could do to find k.

The magnets produce a uniform horizontal magnetic field in the region between them. A copper wire DE is connected in the circuit shown in Figure 2 and is clamped horizontally at right angles to the magnetic field.

Figure 3 shows a simplified plan view of the copper wire and magnets.

When the apparatus is assembled with the switch open, the reading on the electronic balance is set to 0.000 g. This reading changes to a positive value when the switch is closed.

Which of the following correctly describes the direction of the force acting on the wire DE due to the magnetic field when the switch is closed?

Tick (✓) the correct box.

Label the poles of the magnets by putting N or S on each of the two dashed lines in Figure 3.

Define the tesla.

The magnets are 5.00 cm long. When the current in the wire is 3.43 A the reading on the electronic balance is 0.620 g.

Assume the field is uniform and is zero beyond the length of the magnets.

Calculate the magnetic flux density between the magnets.