A full set of ten original structured questions in the style of Paper 4, covering the whole of Magnetic fields: field lines, the force on a conductor and on a moving charge, the Hall effect, fields due to currents, and electromagnetic induction. Several questions chain one idea into the next within the topic. Each is linked to its lessons; attempt them all, then reveal the worked solutions.
A straight wire passes at right angles through the uniform field between the poles of a magnet, as shown in Fig. 1.1. The flux density is 0.25 T and the length of wire in the field is 4.0 cm.
(a) State two rules that magnetic field lines always obey. [2]
(b) Define magnetic flux density. [2]
(c) The wire carries a current of 3.0 A. Calculate the force on the wire. [2]
(d) State the direction of this force, and the rule you used. [2]
(e) The wire is now turned so that the current makes an angle of 30° with the field. Calculate the new force. [2]
(f) State the angle between the current and the field for which the force is a maximum. [1]
(g) State the value of the force when the current is parallel to the field. [1]
A horizontal wire of length 5.0 cm rests on a top-pan balance and lies at right angles to a horizontal magnetic field of flux density 0.18 T. When a current of 4.5 A passes through the wire, the magnetic force on it acts vertically.
(a) Calculate the magnetic force on the wire. [2]
(b) Calculate the change in the balance reading, in grams, that this force produces. [2]
(c) Define the tesla. [2]
(d) Express the tesla in SI base units. [2]
(e) State and explain the effect on the force of doubling the current. [2]
(f) State what reading change would be seen if the wire were rotated to lie along the field. [1]
An electron travelling at 3.0 × 10⁶ m s⁻¹ enters a uniform magnetic field of flux density 2.0 mT at right angles to the field. (electron mass 9.11 × 10⁻³¹ kg, charge 1.6 × 10⁻¹⁹ C)
(a) Explain why the electron follows a circular path at constant speed. [2]
(b) Calculate the magnitude of the magnetic force on the electron. [2]
(c) Show that the radius of the path is given by r = mv/BQ, and calculate r. [3]
(d) Calculate the period of the circular motion. [2]
(e) State and explain the effect on the radius of doubling the speed. [2]
(f) State the effect on the period of doubling the speed. [1]
A slice of a current-carrying semiconductor is placed in a magnetic field perpendicular to its largest face. A steady Hall voltage appears across the slice.
(a) Explain how the Hall voltage is set up. [3]
(b) The Hall voltage is Vₐ = BI / (ntq). A slice has charge-carrier density n = 1.0 × 10²² m⁻³, thickness t = 0.50 mm, and carries a current of 20 mA. The Hall voltage is 2.4 mV. Calculate the flux density. [3]
(c) Explain why a semiconductor, rather than a metal, is used for a Hall probe. [2]
(d) State what a Hall probe is used to measure. [1]
(e) State the effect on the Hall voltage of doubling the flux density. [1]
Fig. 5.1 shows a velocity selector. Positive ions pass through a region of crossed electric and magnetic fields. The electric field is produced by parallel plates 2.0 cm apart with a potential difference of 600 V across them, and the magnetic field has flux density 0.050 T.
(a) Show that an ion travels straight through only if its speed is v = E/B. [2]
(b) Calculate the electric field strength between the plates, and hence the selected speed. [3]
(c) Explain what happens to ions that are travelling faster than the selected speed. [2]
(d) The selected ions, each of charge +1.6 × 10⁻¹⁹ C, then enter a magnetic field of flux density 0.20 T and move in a circle of radius 8.0 cm. Calculate the mass of an ion. [3]
(e) State the name of an instrument that uses this arrangement. [1]
Two long straight parallel wires P and Q are a few centimetres apart and carry currents in the same direction.
(a) Describe the shape of the magnetic field around a single long straight wire, and how its direction is found. [2]
(b) State whether P and Q attract or repel, and explain why in terms of their fields. [3]
(c) State what happens to the force if the current in Q alone is reversed. [1]
(d) State what happens to the force if the currents in both P and Q are reversed. [1]
(e) Describe the magnetic field inside a long solenoid. [2]
(f) State the effect on this field of inserting a soft iron core. [1]
A flat coil of 200 turns, each of area 1.5 × 10⁻³ m², lies with its plane perpendicular to a magnetic field. The flux density increases steadily from 0 to 0.40 T in a time of 0.20 s.
(a) Define magnetic flux. [1]
(b) Calculate the change in magnetic flux linkage. [3]
(c) Calculate the e.m.f. induced in the coil. [2]
(d) State Faraday's law of electromagnetic induction. [2]
(e) State Lenz's law, and the conservation principle it expresses. [2]
(f) State the effect on the induced e.m.f. of doubling the number of turns. [1]
Fig. 8.1 shows how the magnetic flux linkage through a search coil varies with time as a magnet is moved near it.
(a) State how the induced e.m.f. is obtained from this graph. [1]
(b) Calculate the induced e.m.f. during the first 0.30 s. [3]
(c) State the induced e.m.f. between 0.30 s and 0.70 s, and explain your answer. [2]
(d) Compare the size and sign of the e.m.f. after 0.70 s with that in the first 0.30 s. [2]
(e) State the general effect on the induced e.m.f. of moving the magnet more quickly. [2]
A metal rod of length 0.25 m rests on two horizontal rails and is pulled along them at a steady 4.0 m s⁻¹. A uniform magnetic field of flux density 0.30 T is perpendicular to the plane of the rails, as in Fig. 9.1. The rails are joined by a resistor of resistance 0.50 Ω.
(a) Show that the e.m.f. induced across the rod is given by ε = BLv, and calculate its value. [3]
(b) Calculate the current driven through the resistor. [2]
(c) The current in the rod lies in the magnetic field. Calculate the force on the rod due to this current. [2]
(d) State the direction of this force relative to the motion, and name the law that gives it. [2]
(e) Explain, using energy, why a force must be applied to keep the rod moving at constant speed. [2]
(f) State and explain the effect on this opposing force of doubling the speed. [2]
This question links three lessons of the topic. A long solenoid carries a current and a coil of 500 turns is wound around its middle.
(a) Describe the magnetic field inside the solenoid, and state the effect of placing a soft iron core inside it. [2]
(b) The current is switched off, and the flux linkage of the 500-turn coil falls from 0.080 Wb to zero in 0.040 s. Calculate the average e.m.f. induced. [3]
(c) State the direction of the induced current relative to the change, and the law used. [2]
(d) An electron now enters the solenoid's field of flux density 0.015 T at 2.0 × 10⁶ m s⁻¹, at right angles to the field. Calculate the radius of its circular path. [3]
(e) State and explain the effect on this radius of doubling the flux density. [2]
(f) State why the magnetic force on the electron does not change its speed. [1]
Mark this once you have attempted all ten questions and checked your working against the solutions. Revealing the solutions alone does not count.