Electromagnetism. Investigations

Electromagnetism Investigations Autumn 2015

ELECTROMAGNETISM Investigations Table of Contents Magnetic effect of an electric current* 2 Force on a current-carrying conductor in a magnetic field* 6 Faraday s law of electromagnetic induction* 7 Lenz s law 9 Induction motor Arago s disc 11 Mutual induction 12 Transformer 14 Self-induction (back emf) 15 Appendix 1: Force on a current-carrying conductor 18 in a magnetic field Appendix 2: Electromagnetic induction 19 Appendix 3: Lenz s law 21 Appendix 4: Eddy currents in a copper plate 22 Appendix 5: Electromagnetic induction (with dataloggers) 23 Appendix 6: Pending changes to SI Base Units 24 *Denotes it is suitable for Junior Cycle and TY students Page 1

INVESTIGATING THE MAGNETIC EFFECT OF AN ELECTRIC CURRENT (Oersted s Experiments) In 1820 Oersted established a clear connection between electricity and magnetism. He discovered that an electric current in a wire produced a magnetic effect. Apparatus 6 V power supply, a large (e.g. an orienteering compass), a long lead. 1. Place the lead over the compass so that it is parallel to the compass needle as shown in Arrangement A. 2. Turn on the switch and allow a current to flow for 1 or 2 seconds. 3. Observe and record the action of the compass needle. Arrangement A 4. Repeat the experiment only this time place the lead perpendicular to the compass needle as in Arrangement B. 5. Observe and record the action of the compass needle this time. Arrangement B Issues to be explored Explain how the needle moves in one arrangement but not the other? Repeat Arrangement A, i.e. let wire run parallel to the compass needle, only this time place the compass above the wire. What is the effect on the compass needle? Repeat Arrangement A, i.e. let wire run parallel to the compass needle, only this time change the direction of the current back and forth a number of times. What is the effect on the compass needle? Repeat Arrangement B i.e. let the wire run perpendicular to the compass needle, only this time change the direction of the current back and forth. What is the effect on the compass needle? Page 2

The compass needle moves when the current is parallel to the needle direction and then remains perpendicular to the wire. It may give an initial rotation when the current is perpendicular to the compass needle but will then remain perpendicularly aligned. We conclude that a magnetic field is induced by current and that the magnetic field direction is perpendicular to the direction of the current. We observed that the direction of the current affects the direction of the compass needle and conclude that the direction of induced the magnetic field is determined by the current direction. Insert a resistor in the circuit for student use. Extension: Investigating the direction and shape of the induced magnetic field. Let the wire run perpendicularly through a solid stage e.g. a CD. Now move a single plotting compass around the platform and see can you determine the direction and shape of the magnetic field. Current Magnetic field RIGHT HAND GRIP RULE Note the circular magnetic field We can use what is known as the right hand grip rule to determine the direction of the magnetic field, if we arrange our right hand as in the diagram, so that the thumb points in the direction of positive conventional current then the fingers point in the direction of the magnetic field. RIGHT HAND GRIP RULE Page 3

Issues to be explored What shape would the magnetic field take if instead of a straight wire we had a single loop of coil? We can apply the right hand rule to each side of the coil, the current goes up one side of the coil and down the other and we see that inside the coil the direction of the field is the same due to each side. What would the shape of the magnetic field be if we had a coil of an increased number of turns? We can apply the right hand grip rule to each turn and we see that the direction of the field is the same all along the inside of the coil. The magnetic field generated by a current carrying long straight coil is the same as the magnetic field of a bar magnet so a coil of wire with a current flowing through it could be used as a magnet, we call such a magnet an electromagnet. The electromagnet has the added advantage that it can be turned on and off at will. Applications of the magnetic effect of an electric current include: Motors, doorbells, electromagnetic cranes (for lifting scrap iron), magnetic hotel door card keys, etc. Page 4

WORKSHEET ON THE MAGNETIC EFFECT OF AN ELECTRIC CURRENT - Teacher copy 1. When the wire is placed parallel to the north south direction of the plotting compass does the needle move?..yes, because the magnetic field due to the wire is perpendicular to the wire and much stronger than the earth s magnetic field. 2. When the wire is placed perpendicular to the north south direction of the plotting compass does the needle move?...no, because the compass is already pointing in the direction of the magnetic field due to the current. 3. When the wire is placed parallel to the north south direction of the plotting compass and the direction of the current changes does the needle move?..yes, the compass needle constantly changes direction as the current changes direction, this shows that the direction of the current determines the direction of the field. 4. When the wire is placed perpendicular to the north south direction of the plotting compass and the direction of the current changes does the needle move?...yes, the compass needle flips back and forth but the direction is always perpendicular to the wire. 5. Let the wire run perpendicularly through a solid stage e.g. a CD Now move a single plotting compass around the platform and see can you determine the shape of the magnetic field?...yes, the field is clearly circular in shape around the wire. WORKSHEET ON THE MAGNETIC EFFECT OF AN ELECTRIC CURRENT - Student copy 1. When the wire is placed parallel to the compass needle, how does the needle move? 2. When the wire is placed underneath the compass and parallel to the compass needle how does the needle move? 3. When the wire is placed perpendicular to the compass needle, how does the needle move?. 4. When the wire is placed parallel to the compass needle and the direction of the current changes, how does the needle move?. 5. If the wire is placed perpendicular to the compass needle and the direction of the current changes does the needle move?... 6. Let the wire run vertically through a solid stage e.g. a CD Now move a single plotting compass around the platform and see can you determine the shape of the magnetic field?. Page 5

INVESTIGATING THE FORCE ON A CURRENT- CARRYING CONDUCTOR IN A MAGNETIC FIELD Apparatus 6 V power supply, 10 resistor (5 W), aluminium foil, U-shaped alnico magnet. 6 V 10 U-shaped magnet S N Aluminium foil 1. Set up the apparatus as shown with the foil at right angles to the magnetic field. 2. Close the switch, or complete the circuit, and observe the aluminium foil. 3. Reverse the direction of the current flowing in the foil. 4. Observe and record what happens. 5. Reverse the direction of the magnetic field. 6. Observe and record what happens to the foil when a current flows. See appendix 1. The 10 resistor should be rated at 5 watts. Overheating will occur if a 0.25 W or 0.5 W resistor is used. The foil moves when a current flows through it. Reversing the direction of the current or the magnetic field reverses the direction of the movement of the foil. Conclusion When a current flows in the foil, it experiences a force. This causes it to move. The direction of the force can be found using the second right hand rule. (See: https://en.wikipedia.org/wiki/lorentz_force ) Applications This is the principle of operation of the electric motor, the moving coil meter and the moving coil loudspeaker. Sonometer connected to wave generator with a Ushaped magnet under the sonometer wire Simple motor https://www.youtube.com/watch?v=zodboryf1hm Page 6

INVESTIGATING THE FARADAY S LAW OF ELECTROMAGNETIC INDUCTION Apparatus Bar magnet, coil with 800 turns, galvanometer. Magnet Coil of wire Galvanometer 1. Set up the apparatus as shown. 2. Push the magnet into the coil and note the deflection of the galvanometer. 3. Pull the magnet out of the coil and note the deflection. 4. Repeat, moving the magnet with different speeds, and observe what happens to the deflection (direction and size) on the galvanometer: As you move the magnet into the coil (a) quickly, (b) slowly If you change the direction of motion of the magnet If you turn the magnet around (poles swapped) If you use a coil with more (less) turns If you use a more powerful magnet (you may tape two magnets together, with like poles side by side) Issues to be explored What energy conversions take place in this experiment? Faraday s Law of Electromagnetic Induction implies that to generate an e.m.f. in a coil the magnetic flux through the coil must be changing. How is that done in this experiment? How do you make the flux change more rapidly? If you double the number of turns in the coil does the e.m.f. double? State Faraday s Law of electromagnetic induction To explain accurately what happens in this experiment the concept of magnetic flux is used. Define what is meant by magnetic flux. Page 7

A current will flow in the coil if there is a complete circuit. When a current flows in the coil it behaves like a bar magnet. If the N pole of the magnet is entering the coil, explain why, using the Law of Conservation of energy, the end of the coil facing the magnet must also be a N pole. Observation The faster the magnet is moved, the greater the deflection of the galvanometer. Conclusion E = IR. The coil has a fixed resistance. An increase in current indicates a corresponding increase in emf. The faster the motion of the magnet the greater the current indicated by the galvanometer, which implies a greater emf induced. This may also be shown by using a stronger magnet or taping two magnets together, with like poles side by side. The resulting increase in flux ( produces a greater deflection. See appendix 2. Page 8

INVESTIGATING LENZ S LAW Apparatus Copper pipe, plastic pipe, stopwatch, strong neodymium magnet, piece of unmagnetised neodymium or iron, (same size as magnet). Magnet Magnet Copper pipe Plastic pipe /Observations 1. Drop the neodymium magnet down through the length of copper pipe held vertically and note the duration of fall. 2. Repeat the same procedure using the plastic tube. 3. Compare the time taken for the magnet to fall through both tubes? 4. In which tube was the overall velocity of the magnet least? 5. In which direction does the force of gravity act? 6. In which direction is the force, causing the magnet to slow down, acting? Further Discussion: 1. You have already learned about the nature of magnetic fields: they have magnitude and direction. You also know that there is a magnetic field produced whenever there is an electric current in, let s say, a copper wire or loop. Do you think that the moving magnet has induced some kind of electric current in the copper? 2. If there is an electric current induced in the copper, it should create a magnetic field. This newly created magnetic field exerts a force on the falling magnet. Does it oppose the motion of the magnet? (Hint: the magnet slows down). Page 9

Observation The time taken for the magnet to fall down through the copper tube is much greater than the time taken for the magnet in the plastic tube or the piece of neodymium in either tube. Explanation The moving magnet induces an electric current in the copper. This current creates a magnetic field that exerts a force to oppose the motion of the magnet and hence slows it down. The copper and plastic pipes used are available from plumbing suppliers. As an alternative to copper pipe use an aluminium rail Page 10

INVESTIGATING THE INDUCTION MOTOR ARAGO S DISC Apparatus Aluminium or copper disc (centre punched), strong magnet, pivot. Rotating magnet Spinning spiral disc & neodymium magnet Disc Pivot 1. Place the disc on the pivot. 2. Move the magnet quickly in a circular motion above the rim of the disc. Issues to be explored 1. What do you observe happening to the disc as the magnet rotates above it? 2. In what direction does the disc rotate? 3. Now move the magnet quickly in a circular motion above the rim of the disc, in the opposite direction to that in step 2. 4. What do you notice about the rotation of the disc this time? 5. Why does this happen? Alternatively use a soft drinks can balanced on the tip of a pencil, supported by blu-tack & neodymium magnet The moving magnet induces a current in the disc. This current creates a magnetic field that exerts a force to oppose the motion of the magnet. The magnet exerts an equal and opposite force and the disc rotates. The relative motion between the magnet and the disc is reduced. For more details visit: https://vimeo.com/20847392 A copper or aluminium calorimeter balanced on a point could also be used for this demonstration. This demonstration is from the Applied Electricity section of the syllabus Applications Induction motors are used in speedometers, tachometers and some electric clocks. They are also used as large motors in factories as they do not have brushes, commutators, etc. to wear out. Page 11

INVESTIGATING MUTUAL INDUCTION Apparatus Coils of wire 400 and 800 turns, galvanometer, soft iron core, 6 V battery. 6 V 1. Set up the apparatus as shown with the two coils side by side. 2. Connect one coil to the 6 V supply. 3. Close the switch a deflection is seen on the galvanometer. 4. Open the switch a larger deflection is observed. 5. Repeat moving the coils closer together and note the galvanometer deflection. 6. Repeat inserting a soft iron core into the coils. Move the coils closer together and note the galvanometer deflection. Each time the circuit is completed or broken, a deflection is observed on the galvanometer. The deflection at the break is greater than at the make. Conclusion At the make and break of the circuit there is a change in the magnetic flux linking the coils and so an emf is induced in the secondary coil. The break is faster than the make and so the rate of change of flux is greater at the break. This creates a greater emf and so a larger current is produced at the break of the circuit. If both coils are mounted on a shared iron core a much greater deflection is obtained. This is dφ because the magnetic flux Φ has been increased and, from Faraday s law, E dt 6 V Iron Page 12

INVESTIGATING MUTUAL INDUCTION CONTINUED Apparatus 6 V a.c. power supply, coils of wire 400 turns and 800 turns, soft iron core, two a.c. voltmeters. 400 turns 800 turns V in V V V out 1. Set up the apparatus as shown above. 2. Switch on the 6 V a.c. supply. Issues to be explored Record the readings obtained from each voltmeter? What happens to the output reading V out when the coils are moved closer together? Insert the U-shaped iron core and record V out. Complete the full core and record V out. What can you conclude? The a.c. produces a constantly changing magnetic field. Hence an emf is continuously induced in the other coil. The iron core increases the magnetic flux. Page 13

INVESTIGATING THE TRANSFORMER Primary coil N p Iron core Secondary coil N s V in V V V out 1. Set up the apparatus. 2. Read the voltages on both coils. 3. Read the number of turns on both coils, N p and N s. 4. Switch the coils and repeat. Results V in / V V out / V V V in out N N p s It is found that Vin V out N N P s Applications Transporting energy/power, Mobile phone chargers, Televisions, Computers, Power stations. For more visit: https://en.wikibooks.org/wiki/basic_electrical_generation_and_distribution or visit: http://c21.phas.ubc.ca/article/transformers Page 14

INVESTIGATING SELF-INDUCTION (BACK EMF) (a) Apparatus 6 V a.c. power supply, coil of wire with 1200 turns, soft iron core, 6 V filament lamp. Iron core 6 V 1. Connect the bulb, coil and a.c. supply in series. 2. Switch on the power supply and observe the lamp. 3. Insert the iron core into the coil and observe the lamp. 4. Explain your observations. The a.c. produces a changing magnetic field in the coil. This induces an emf and hence a current that opposes the applied current. The iron core increases the magnetic flux and hence the induced opposing current is increased. The resultant current in the circuit is reduced and the bulb becomes dimmer. This is the principle on which large dimmer switches for stage lights in theatres operate. If this circuit is set up using a d.c. power supply, no dimming occurs with the core in the coil as there is no changing magnetic field. This effect is best demonstrated by putting the coil on the completed transformer core. This gives a much greater change in magnetic flux and so a larger opposing current. Page 15

(b) Apparatus 1.5 V cell /Suitable d.c. power supply, electric motor/toy electric car, ammeter. M Motor 1.5 V A 1. Connect the switched d.c. power supply, ammeter, and motor in series. 2. Turn on the digital multimeter and set to dc A. [Remember: Use the 'COM' and the 'A' ports]. **Any d.c milli-ammeter will suffice ** 3. Switch on the power supply (to 1.5 V approx.) 4. What current is displayed on the digital multimeter (or your milli-ammeter)? 5. Is the voltage displayed on your power supply? If so, make a note of its value. * If the power supply does not display voltage or to check its accuracy connect a voltmeter in parallel with the power supply. * 6. Is the motor turning freely? 7. Place a finger on the rotating wheel to slow the rotations. 8. When the wheels slow down, do you notice any change on the digital ammeter reading? 9. Why do you think this may have occurred? 10. Did the voltage value change? 11. Did you expect the voltage to change? 12. What conclusion can you draw from your investigation? Explanation When the coil of the motor is rotating in the magnetic field, a current is induced that opposes the applied current. If the motor slows down, the rate of magnetic flux change is reduced. This means that the induced e.m.f. is smaller. Therefore the induced opposing current is reduced and hence the resultant current increases. This is why many large motors have starter resistors incorporated. It also explains why motors burn out if they cannot turn while the current is flowing. There is no opposing induced e.m.f. so a larger current flows. A scaled-electric car motor works well. Applying friction to the rotating wheels slows down the motor and a noticeable increase in the resultant current is observed. This model of motor can stimulate the interest of a pupil. It connects their past childhood with physics in a fun way. Page 16

(c) Apparatus 6 V battery, 90 V neon lamp/phase tester, coil with 1200 turns, soft iron core. Iron core 90 V Neon lamp 6 V 1. Connect the switch, coil and 6 V battery in series. 2. Connect the neon lamp/phase tester in parallel with coil. 3. Switch on the power supply 4. Close the switch and observe the neon lamp. 5. Open the switch and observe the neon lamp. 6. Record your observations. 7. Explain your observations. Explanation As the circuit is switched on or off, there is a changing magnetic field in the coil. This causes an emf to be induced. With the large number of turns and the iron core, this emf is greater than 90 V and so the lamp lights. The magnetic field is only changing when the circuit is being switched on or off. The flash is brighter on the break because the magnetic field takes longer to build up than to collapse. ** The standard laboratory Neon lamp may also be replaced with a common 220-240Vac Snap In Neon Red (pictured opposite). Connection is via two 1/4" (6.35 mm) push on blade terminals separated by a plastic insulator. Overall length is 33 mm and lens diameter is 12 mm. Purchased in Maplin Stores - cost 2. The only noticeable 'flicker of light' when using this lamp occurred when the circuit was switched off, reinforcing that the magnetic field collapses quicker than it builds and hence with this quicker change of magnetic field - a larger e.m.f. is induced. For more visit: https://www.youtube.com/watch?v=pkksco9egbq Page 17

Appendix 1 INVESTIGATING THE FORCE ON A CURRENT-CARRYING CONDUCTOR IN A MAGNETIC FIELD Apparatus Signal generator, 10 (5 W) resistor, ammeter, U-shaped magnet, aluminium foil. A Signal generator U-shaped magnet 10 Aluminium foil 1. Set the signal generator at the square wave option. 2. The aluminium foil is connected in series with an ammeter and a high wattage 10 protective resistor to the low impedance output of the signal generator as shown. 3. Ensure that the current does not exceed 0.4 A (or lower if indicated on the generator). 4. Set the frequency at 2 Hz and observe the foil. 5. Gradually increase the frequency. Observe the foil and listen. 6. Remove the magnet and observe. Observation The foil moves up and down. At frequencies >100 Hz, sound can be heard from the foil. Explanation When a current from the signal generator flows through the foil, it experiences a force. Since the current is a.c. the direction of the force changes with the direction of the current and so the foil moves up and down. At high frequencies the vibrating foil produces sound (as in the moving-coil loudspeaker). If the magnet is removed, the foil does not experience a force and so motion and sound disappear. A small radio/walkman with an earphone can also be used. Set the signal generator at the amplifier option. The output from the earphone is fed into the amplifier of the signal generator. The foil is connected to the low impedance output of the signal generator as shown. When the radio is turned on, the sound can be heard from the vibrating foil. A Radio Signal generator 10 Aluminium foil U-shaped magnet Page 18

Appendix 2 INVESTIGATING ELECTROMAGNETIC INDUCTION Apparatus Coil of wire (10 000 turns), red LED, green LED, magnet.. Magnet Coil of 1. Connect the LEDs to a coil of wire as shown. 2. Push the magnet into the coil and observe the LEDs. 3. Withdraw the magnet from the coil and observe the LEDs. Issues to be explored Why are both LEDs not bright at the same time? Use Faraday s Law to explain what happens Use Faraday s Law to explain why neither LED lights if the magnet is moving slowly Would the number of turns in the coil make any difference? Use Faraday s Law to explain why a powerful neodymium magnet works best in this experiment Give two reasons why LEDs are more suitable in this experiment than small filament torchlight bulbs Page 19

Observation As the magnet is moved into the coil one of the LEDs lights and as it is being withdrawn the other LED lights. Explanation As the magnet moves in or out of the coil, the magnetic flux linking the coil changes. An emf is induced in the coil and current flows in the circuit. This current lights the LED. The alternate lighting of the red and green LEDs arises because of Lenz s law. The induced current opposes the change causing it. The current flows in the opposite direction when the motion of the magnet is reversed. Since the LEDs must be forward biased to conduct, only one can light at any one time. Conclusion A changing magnetic flux in a coil induces an emf. The direction of the current depends on the direction of the motion of the magnet. Alternatively insert a neodymium magnet into a plastic cylindrical container surrounded by a coil of about 500 turns connected to an LED. Shake the container and observe the LED. Issues to be explored What happens to the LED as the magnet moves up and down the tube? Use Faraday s Law to explain what happens Use Faraday s Law to explain why the LED does not light if the magnet is moving slowly Would the number of turns in the coil make any difference? Use Faraday s Law to explain why a powerful neodymium magnet works best in this experiment Explain why an LED is more suitable in this experiment than a small filament torchlight bulb Page 20

Appendix 3 INVESTIGATING LENZ S LAW Apparatus Aluminium ring, magnet, thread, retort stand. Thread Thread Magnet Aluminium ring 1. Suspend the ring from the retort stand, using two pieces of thread for stability. 2. Move one end of the bar magnet towards and into the ring. 3. Observe and record what happens to the ring. 4. Hold the magnet in the ring and quickly pull it away. 5. Observe and record what happens to the ring. 6. Explain your observations. Observation When the magnet moves, the ring responds by moving in the same direction. Explanation The moving magnet induces a current in the ring. This current creates a magnetic field that exerts a force to oppose the motion of the magnet. The magnet exerts an equal and opposite force on the ring and so the ring moves as observed. Page 21

Appendix 4 INVESTIGATING EDDY CURRENTS IN A COPPER PLATE Apparatus Use a neodymium magnet as the bob of a pendulum. Suspend two such pendulums from a metre stick clamped in a horizontal position. Ensure that both pendulums can swing freely with a clearance of 3 or 4 mm above a table. Place a copper plate under one pendulum. Cover it and the rest of the table with a sheet of card before any student sees the apparatus. Set the pendulums swinging at the same instant with the same initial amplitude. Issues to be explored Is there a difference between the pendulums in terms of: (a) the duration of the oscillations and, (b) the number of oscillations? Why? : Eddy currents are induced in the copper plate which by Lenz s law opposes the oscillation of the magnet that passes over it. Hence this magnet comes to rest much sooner than the one that doesn t have a copper plate under it. Page 22

Appendix 5 Electromagnetic Induction (with dataloggers) Apparatus: 100 milli-amp current sensor, datalogger, computer, coil, magnet Connect a 100 milli-amp current sensor to a datalogger and to a coil. Connect the datalogger to a laptop computer. Launch the graphing software and set it to record with a high sampling rate for a second after the trigger value is reached. Save the graph. A single pulse of alternating current is generated when a magnet falls once through a coil as shown. A soft landing for the magnet needs to be provided. Repeated hard blows to a magnet will reduce its strength. A typical outcome is shown opposite. Current is on vertical axis, time on horizontal. Use the various analysis tools of the software to answer the following questions: Issues to be explored (a) What is the height of the peak in milli-amps? (b) What is the depth of the trough in milli-amps? (c) Which is greater and why? (d) What does the graph tell you about 1. The magnitude of the e.m.f. (voltage) as the magnet enters and leaves the coil 2. The direction of the e.m.f. as magnet enters and leaves the coil Use the Laws of Electromagnetic Induction to explain 1. and 2. (e) What is the duration (in milli-seconds) of the peak? (f) What is the duration (in milli-seconds) of the trough? (g) Which is longer and why? (h) Calculate the area enclosed by the peak and that enclosed by the trough. (i) Which is bigger and why? (j) What physical quantity is represented by the area of the peak? Extension activities 1. If the coil is replaced with one which has a different number of turns of wire, what is the effect, if any? 2. If the magnet is replaced with a stronger magnet, what is the effect, if any? : Answers: (c ) depth of trough is greater, because magnet is accelerating and so greater rate of change of magnetic flux. (f) duration of peak is greater, because magnet accelerating and so the trough is completed quicker. (1.) bigger pulse of current. (2.) bigger pulse of current. Page 23

Appendix 6 Pending changes to SI Base Units A subcommittee of the International Committee for Weights and Measures (CIPM) has proposed revised formal definitions of the SI base units, which are being examined by the CIPM and which will likely be adopted at the 26th General Conference on Weights and Measures in the autumn of 2018. Below are some of the most common. The second Current definition: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. Proposed definition: The second, s, is the unit of time; its magnitude is set by fixing the numerical value of the ground state hyperfine splitting frequency of the caesium-133 atom, at rest and at a temperature of 0 K, to be equal to exactly 9 192 631 770 when it is expressed in the unit s 1, which is equal to Hz. The metre Current definition: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second. Proposed definition: The metre, m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299 792 458 when it is expressed in the unit m s 1. The kilogram Current definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Proposed definition: The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.62606X 10 34 when it is expressed in the unit s 1 m 2 kg, which is equal to J s. Two such spheres have been constructed, at a cost of $3.2 million each The ampere Current definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 10 7 newton per metre of length. Proposed definition: The ampere, A, is the unit of electric current; its magnitude is set by fixing the numerical value of the elementary charge to be equal to exactly 1.60217X 10 19 when it is expressed in the unit A s, which is equal to C. Page 24