4.3 Current-carrying conductor in a magnetic field

4.3 Current-carrying conductor in a magnetic field
Battery car Force on a current-carrying conductor Check-point 5 Check-point 6 Application: electric motors Check-point 7 Application: moving-coil loudspeakers Check-point 8 1 2 3 Book 4 Section 4.3 Current-carrying conductor in a magnetic field 1

Book 4 Section 4.3 Current-carrying conductor in a magnetic field
Battery car Connect a battery and two strong magnets with a wire. The battery starts rolling with the magnets like a car! Can you explain why? Book 4 Section 4.3 Current-carrying conductor in a magnetic field

1 Force on a current-carrying conductor
We know that current-carrying wire can deflect a compass needle (i.e. force exists). By Newton’s third law, we expect an opposite force to act on the current-carrying wire by the magnet. What happens if the wire, instead of the magnet, moves freely? Expt 4d Force on a current-carrying conductor Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Experiment 4d Force on a current-carrying conductor Set up the apparatus. Switch on power supply and observe the motion of the rider. Repeat step 1 by turning magnets around. Repeat step 1 by reversing current direction. Video 4.6 Expt 4d - Force on a current-carrying conductor Book 4 Section 4.3 Current-carrying conductor in a magnetic field

a Fleming’s left-hand rule A piece of wire held between the poles of a magnet: When current flows through the wire, an upward magnetic force acts on it. If direction of either current or external magnetic field is reversed, wire moves downwards. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

a Fleming’s left-hand rule
Hold the thumb and the first two fingers of the left hand at right angles. The thumb gives the direction of the magnetic force F, if the 1st finger points in the same direction as the external magnetic field B, and the 2nd finger in the same direction as the current I. Example 7 Deflection of electron in a magnetic field Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 7 Deflection of electron in a magnetic field An electron enters a magnetic field: (a) What is the direction of current due to the moving electron before entering the B-field? To the left ∵ e– carries a –ve charge ∴ opposite to current direction Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 7 Deflection of electron in a magnetic field (b) How will the electron be deflected inside the magnetic field? Downwards (by Fleming’s left-hand rule, a downward magnetic force acts on it.) Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 5 – Q1 A wire carries a current flowing into the paper in a B-field pointing downwards. What is the direction of the magnetic force acting on the wire? A ↑ C ← B ↓ D → Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 5 – Q2 Conductor AB is connected to a battery and placed between the two poles of a horseshoe magnet. Indicate the direction of the magnetic force acting on the AB. (a) (b) F No magnetic force acts on AB (∵current // B-field) Out of the paper Book 4 Section 4.3 Current-carrying conductor in a magnetic field

b Factors affecting magnetic force Expt 4e Effect of current on magnetic force Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Experiment 4e Effect of current on magnetic force Set up a current balance. Adjust the position of the wire until it is balanced. Set the electronic balance to zero. Switch on the current. Pass different currents through the wire. Find out how the magnetic force is related to the current. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Experiment 4e Effect of current on magnetic force Fix the current. Place more pairs of slab-shaped magnets one by one round the arm. Record the corresponding balance readings. Find out how the magnetic force is related to length of wire inside the magnetic field. Video 4.7 Expt 4e - Effect of current on magnetic force Book 4 Section 4.3 Current-carrying conductor in a magnetic field

b Factors affecting magnetic force
Expt 4f Effect of magnetic field strength on magnetic force Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Experiment 4f Effect of magnetic field strength on magnetic force Set up a current balance. Pass a current through the solenoid and place the current-carrying arm inside. 3. Pass a fixed current through wire. Adjust the flat solenoid current and record the corresponding readings. How does the magnetic force change with the B-field? Video 4.8 Expt 4f - Effect of magnetic field on magnetic force Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Magnetic force  if current  length of wire inside the magnetic field  magnetic field strength  Book 4 Section 4.3 Current-carrying conductor in a magnetic field

F  I (constant B and l ) (1) F  l (constant B and I ) (2) F  B (constant I and l ) (3)  F  BI l or F = k  BI l (4) k : constant F = BI l Setting k = 1, Example 8 Measuring force using a digital balance Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 8 Measuring force using a digital balance Magnets P and Q (7 cm long) are rested on an balance. A wire (with XY = 5 cm) is suspended between them. The balance reads g when no current flows through the wire, and g when 2-A current flows in the XY direction. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 8 Measuring force using a digital balance (a) Direction of force acting on the wire? Reading   downward force on magnets  force on wire acts upwards (∵ the forces form an action-and-reaction pair) (b) Pole of inner face of P ? (deduce it by Fleming’s left-hand rule) Magnetic field: from P to Q ∴ inner face of P is the north pole. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 8 Measuring force using a digital balance (c) Magnitude of magnetic field by P and Q = ?  B = F I l = (146.5 – 145)(0.01) (2)(0.05) F = BI l = 0.15 T (d) A 3-A current flows through the wire in YX direction. Balance reading = ? Force on the wire = BI l = (0.15)(3)(0.05) = N (downwards)  An upward force acts on the magnet Reading = 145 – 0.0025 0.01 = ≈ g Book 4 Section 4.3 Current-carrying conductor in a magnetic field

When current I and magnetic field B are not at right angles, only the field component  the current (i.e. B sin  ) contributes to magnetic force. Magnetic force that acts on the wire becomes: F = (B sin  )  I l F = BI l sin  Book 4 Section 4.3 Current-carrying conductor in a magnetic field

The direction of magnetic force can still be found by Fleming’s left-hand rule with the middle finger pointing along the current component that  the magnetic field. If current // B-field, sin  = 0  no force is produced Example 9 Calculation of magnetic force Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 9 Calculation of magnetic force A 1.5-m wire carrying a current of 10 A is placed in a magnetic field of 0.2 T. What is the total force on the wire if (a) it is placed at 30 to the field? F = BI l sin  = 0.2  10  1.5 sin 30 = 1.5 N (b) it is placed along the field? Zero (∵ wire // magnetic field) Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 10 Interaction between two parallel current-carrying wires Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 10 Interaction between two parallel current-carrying wires Two long parallel wires, X and Y are 0.1 m apart. Wire X carries a current of 3 A and Y of 2 A. The cross-sectional view of wires: (a) Deduce and mark the direction of the magnetic forces on X and Y due to the current. By Fleming’s left-hand rule, the magnetic force acting on Y is towards X, and that acting on X is towards Y . Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 10 Interaction between two parallel current-carrying wires (b) Magnitude of the magnetic field produced by X at Y = ? (0 = 4  10–7 T m A–1) B = 0I 2r = (4  10–7)(3) 2(0.1) = 6  10–6 T (c) Magnetic force per unit length acting on Y = ? F = BI l = (6  10–6)(2)(1) = 1.2  10–5 N (towards left) Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 6 – Q1 The cross-section of two parallel straight wires Y and Z : Both of them carry current. Draw arrows to show the magnetic forces on each of them. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 6 – Q2 Refer to Example 10: (a) Magnitude of the magnetic field produced by Y at the position of X = ? B = 0I 2r = (4  10–7)(2) 2(0.1) = 4  10–6 T Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 6 – Q2 Refer to Example 10: (b) Magnetic force per unit length on X = ? F = BI l = (4  10–6)(3)(1) = 1.2  10–5 N (towards right) Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 6 – Q2 Refer to Example 10: (c) Which Newton’s law can also solve (b)? Newton’s third law. Forces are an action-and-reaction pair.  same magnitude, opposite directions Book 4 Section 4.3 Current-carrying conductor in a magnetic field

c Magnetic force between two parallel currents
Combining formulae of B = 0I1 2r and F = BI2l Magnetic force between two long straight parallel current-carrying wires: F = 0I1I2l 2r I1 and I2: currents in the two wires l : length of wires r : distance between the wires Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Two current-carrying wires attract each other when the currents are in the same direction; and repel each other when the currents are in opposite direction. Each pair of forces forms an action-and-reaction pair. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

0I1I2l 2r According to , the definition of ampere may be stated as: The ampere (A) is a constant current, which, flowing in two infinitely long thin straight parallel wires, placed 1 m apart in a vacuum, would produce a force between them of 2  10–7 newton per metre of the wire. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

2 Application: electric motors
Electric motor is a device which converts electrical energy to kinetic energy  commonly found in electrical appliances Book 4 Section 4.3 Current-carrying conductor in a magnetic field

a Turning effect on a coil A rectangular coil lies between two poles. Current flows in opposite directions along the two sides of the coil. By Fleming’s left-hand rule, one side is pushed up while the other side down.  the coil turns Book 4 Section 4.3 Current-carrying conductor in a magnetic field

a Turning effect on a coil
Coil starts from horizontal and turns clockwise. When it is vertical, forces act along the same line and cancel each other.  no turning effect But the coil shoots past the vertical by inertia. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

a Turning effect on a coil
After that, turning effect reverses and the coil turns back. As a result, the coil vibrates a few times and comes to rest lying along the vertical. Simulation 4.3 Turning effect on a coil Book 4 Section 4.3 Current-carrying conductor in a magnetic field

b Simple d.c. motors Expt 4g Constructing a model electric motor Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Experiment 4g Constructing a model electric motor Construct a model electric motor. Connect the ‘brushes’ to a d.c. power supply. Switch on the supply and watch the motor rotates. If necessary, give the wooden block a push to set it in motion. Videos 4.9 Expt 4g - Constructing a model electric motor Book 4 Section 4.3 Current-carrying conductor in a magnetic field

b Simple d.c. motors A simple electric motor uses magnetic turning effect on a coil: Current flows through the coil via a pair of carbon brushes. The brushes are pushed against a commutator, or split-ring. The commutator is fixed to the coil and rotates with it. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

b Simple d.c. motors Commutator keeps the coil rotating continuously. When the coil shoots past the vertical by inertia, commutator changes contact from one brush to another. The current through the coil and forces on it are reversed. The coil rotates in the same direction. Simulation 4.4 Simple d.c. motor Example 11 Rotations of a coil Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 11 Rotations of a coil An insulated coil of copper wire placed between the poles of magnets: The coil can rotate about an axis (dotted line). A current passes round the coil in the direction shown. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 11 Rotations of a coil (a) What is the direction of the force acting on sides AB and CD of the coil? Side AB : downward Side CD : upward (b) Why is there no force acting on BC ? ∵ BC // B-field Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 11 Rotations of a coil (c) Describe the motion of the coil. The coil rotates through turn to vertical position, vibrates a few times about the vertical, and come to rest. 1 4 (d) How to change it into an electric motor? Connect the two ends of the coil to a power supply via a commutator and two carbon brushes. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

b Simple d.c. motors Example 12 Battery car Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 12 Battery car Construct a car with a battery, a wire and two circular magnets. Draw the direction of (a) the current between battery and A on magnet X ; (b) the magnetic force acting on A on magnet X . force current Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 12 Battery car (c) If X and Y rotate in the same direction, what is the polarity of the inner side of Y ? Magnetic force acting on B has the same direction as that of A. Also, current flows downwards from B to the battery. By Fleming’s left-hand rule, magnetic field lines of Y points towards the battery.  The inner side of Y is the north pole Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 7 – Q1 Refer to Example 10: Find magnetic force per unit length on Y. (0 = 4  10–7 T m A–1) F = 0I1I2l 2r = (4  10–7)(3)(2)(1) 2(0.1) = 1.2  10–5 N Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 7 – Q2 What is the direction of the magnetic force acting on sides MN and OP ? MN OP A upwards upwards B downwards downwards C upwards downwards D downwards upwards Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 7 – Q3 Which of the following figures correctly shows the magnetic forces acting on the coil (indicated by the thick arrow) as it rotates? A B C D None of the above Book 4 Section 4.3 Current-carrying conductor in a magnetic field

c Factors affecting the turning effect on coils Investigating factors that affect the turning effect on a coil Expt 4h Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Experiment 4h Investigating factors that affect the turning effect on a coil Construct the same model electric motor in Expt 4g. Observe how the turning effect is changed by modifying size of current changing the no. of turns in coil  /  area of coil (within magnetic field) using stronger magnets 4.10 Expt 4h - Investigating factors that affect the turning effect on a coil Video Book 4 Section 4.3 Current-carrying conductor in a magnetic field

c Factors affecting the turning effect on coils
Turning effect on the coil can be  by  current  number of turns in the coil  area of coil (within the magnetic field)  magnetic field Example 13 Factors affecting the turning effects of coils Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 13 Factors affecting the turning effects of coils Rectangular coil PQRS of N turns rotates about a vertical axis ( a uniform B-field B ). The length and width of the coil are l and b respectively. The current through the coil is I. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 13 Factors affecting the turning effects of coils (a) Draw the forces on PS and QR. F F Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 13 Factors affecting the turning effects of coils (b) Express the magnetic force F on PS in terms of B, N, I and l. Force acting on a single coil is BI l. ∵ The coil has N turns ∴ Magnetic force F = NBI l Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 13 Factors affecting the turning effects of coils (c) Find the moment about axis YY’ (in terms of B, I, A, N and . A: area of the coil). Magnitude of force on QR = that on PS Moment about axis YY’ = 2(F  perpendicular distance) = 2(BI lN  sin  ) b 2 = BI lbN sin  = BIAN sin  Book 4 Section 4.3 Current-carrying conductor in a magnetic field

d Practical motors Motors are easily found in many appliances. The structure of a practical motor: Book 4 Section 4.3 Current-carrying conductor in a magnetic field

d Practical motors Coils set at different angles on soft-iron core (armature), each with its own commutator.  smoother and greater turning effect Curved magnets are used  coils  B-field more often  enhances turning effect Book 4 Section 4.3 Current-carrying conductor in a magnetic field

d Practical motors Some motors use electromagnets rather than permanent magnets.  can run on alternating current As current flows backwards and forwards through the coil, magnetic field also changes direction to match it. ∴ motor keeps rotating in the same direction Book 4 Section 4.3 Current-carrying conductor in a magnetic field

3 Application: moving-coil loudspeakers
A moving-coil loudspeaker contains a short free coil inside a cylindrical magnet.  wires  B-field current direction A.c. flows back and forth  coil is pushed in and out  cone vibrates to emits sound waves Simulation 4.5 Working principle of a loudspeaker Example 14 Measuring magnetic field using a current balance Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 14 Measuring magnetic field using a current balance A current balance measures the field of a pair of slab-shaped magnets. A rider of mass 5 g can slide on it. With no current, the wire is just balanced when the rider is above P. A 3-A current flows through the wire in XY direction. The wire is balanced again when the rider slides away from P by 2.8 cm. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 14 Measuring magnetic field using a current balance (a) In which direction does the rider slide? Towards the slab- shaped magnets. (b) Magnitude of torque by the rider = ? Torque = F  d = mg  d = (0.005)(10)  0.028 = 1.4  10–3 N m Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 14 Measuring magnetic field using a current balance (c) Find the magnetic force on the current balance. Fm = magnetic force on current balance In equilibrium, net torque = 0 Fm  0.16 = 1.4  10–3  Fm = 8.75  10–3 N Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Example 14 Measuring magnetic field using a current balance (d) Magnitude of the B-field produced by the slab-shaped magnets = ? Fm = BI l  B = Fm I l = 8.75  10–3 (3)(0.05) = T Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 8 – Q1 A practical motor can rotate smoothly because A its coils consist of a large number of turns. B its coils are wound on a soft-iron armature. C its armature has several coils set at different angles. D it uses electromagnets rather than permanent magnets. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 8 – Q2 An a.c. motor is different from a d.c. motor mainly by using A a soft-iron core instead of a wooden core. B several coils instead of one single coil. C more than one commutator. D electromagnets instead of permanent magnets. Book 4 Section 4.3 Current-carrying conductor in a magnetic field

Check-point 8 – Q3 Suggest four ways to improve the power of a motor.  current  number of turns in the coil  area of the coil Using stronger magnets Book 4 Section 4.3 Current-carrying conductor in a magnetic field

The End Book 4 Section 4.3 Current-carrying conductor in a magnetic field

4.3 Current-carrying conductor in a magnetic field

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