TOPIC 6.3: Magnetic Fields and Forces These notes were typed in association with Physics for use with the IB Diploma Programme by Michael Dickinson

6.3 Magnetic Force and Field 6.3 Introduction. We’ve already studied electric fields and seen that they exist in a region of space surrounding an electric charge This idea can be applied to magnetism. If iron filings are sprinkled on top of a bar magnet, they will show a pattern which traces the lines of magnetic force around the magnet.

6.3 Magnetic Force and Field 6.3 Introduction. The earth behaves like a massive magnet. The south pole of the magnet at the geographic north pole and visa versa. When a compass is positioned anywhere within the Earth’s magnetic field, the needle will orientate itself along the Earth’s magnetic field with it’s magnetic north pole directed towards the Earth’s geographic north pole.

6.3 Magnetic Force and Field State that moving charges give rise to magnetic fields Draw magnetic field patterns due to currents. When an electrical current flows in a piece of wire then a magnetic field is produced around the wire. We can correctly predict the direction of the magnetic field using the “right hand grip rule”

6.3 Magnetic Force and Field The thumb points to the current The fingers show the direction of circular magnetic field. The space between the field lines increase with distance from the wire. Meaning a weaker field the further away.

6.3 Magnetic Force and Field A solenoid is a long wire wrapped around a metal core which produces a magnetic field when electric current is passed through it. They are important because they create controlled magnetic fields and can be used to convert energy into motion. The fingers point in the direction of the current. The thumb points in the direction of the magnetic field lines.

6.3 Magnetic Force and Field Determine the direction of the force on a current-carrying conductor in a magnetic field. When a current-carrying wire is placed in a magnetic field a magnetic force is produced. This usually causes either the magnet or conductor to move. The force will be perpendicular to the current and the magnetic field. We use “Fleming’s left hand rule”

6.3 Magnetic Force and Field Determine the direction of the force on a current-carrying conductor in a magnetic field. This acronym might help: TFC HANDWIRE/MAGNET ThumbThrust (force) Fore fingerField (magnetic) Center fingerCurrent

6.3 Magnetic Force and Field Determine the direction of the force on a current-carrying conductor in a magnetic field. Look at the diagram and identify the direction of the F mag Answer: Down

6.3 Magnetic Force and Field Determine the direction of the force on a current-carrying conductor in a magnetic field. Drawing 3-D sketches can get confusing some times, so there is a convention used. Consider a dart or arrow moving away from you. You would see its tail end. If the dart was moving toward you, you would see its tip.

6.3 Magnetic Force and Field Determine the direction of the force on a current-carrying conductor in a magnetic field. That means the picture from earlier could be drawn like this.

6.3 Magnetic Force and Field Determine the direction of the force on a current-carrying conductor in a magnetic field. The size of the magnetic force, F mag, is proportional to the strength of the magnetic field, B, the size of the current, I, and the length of the wire (that is in the magnetic field), L. IB Formula F = BILsin θ “sin θ ” takes in account for the cases where the conductor and the magnetic field are not perpendicular. Normally when they are perpendicular, the angle between them is 90º and the sin θ disappears.

6.3 Magnetic Force and Field Determine the direction of the force on a charge moving in a magnetic field. When a charged particle moves in a magnetic field it will feel a force. Current is a moving charge. Conventional current is in the opposite direction to the flow of electric charge.

6.3 Magnetic Force and Field Determine the direction of the force on a charge moving in a magnetic field. When a charge enters the magnetic field it will feel a force. This force causes its direction to change. As the direction of motion changes so does the force and it creates a circular motion. Let’s look at this diagram starting at the top.

6.3 Magnetic Force and Field Determine the direction of the force on a charge moving in a magnetic field. The size of the magnetic force, F mag, is proportional to the strength of the magnetic field, B, the velocity of the charge, v, and the size of the charge, q. IB Equation F = qvBsin θ

6.3 Magnetic Force and Field Define the magnitude and direction of a magnetic field. Magnetic field strength, B, is measuered in Tesla, T. It is a vector quantity, so if two magnetic fields interact, vector addition must be used to calculate the resulting magnetic field. We can combine the previous two equations and get the following one. IB Equation F = BILsin θ Permeability of free space = μ 0 = 4π x m/A

6.3 Magnetic Force and Field Solve problems involving magnetic forces, fields and currents. Practice 13 A piece of copper wire is held perpendicular to a magnetic field of strength 0.25 Teslas. The length of the conductor within the field is 10cm. If a current of 8 Amps is allowed to flow in the wire, what is the force on the wire? Answer: 0.2 N

6.3 Magnetic Force and Field Solve problems involving magnetic forces, fields and currents. Practice 14 The same piece of wire is now tilted so that it makes an angle of 30º to the magnetic field. What is now the force on the wire? Answer: 0.1 N

6.3 Magnetic Force and Field Solve problems involving magnetic forces, fields and currents. Practice 15 An electron moves perpendicular to a magnetic field of strength 200µT. As it enters the field it is seen to move through a circular path of radius 20cm. Calculate the speed of the electron. ***Hint: Since the electron moves in a circular path, it undergoes centripetal acceleration and feels a centripetal force. This force comes from the magnetic force. Answer: x 10 6 m/s