PHYS102 Effects of Magnetic ields Dr. Suess March 12, 2007 Magnetic ields 2 Magnetic ields......................................................... 2 Behaior of Poles........................................................ 3 What is Magnetism?...................................................... 4 Magnetic orce 5 Magnetic orce - Qualitatie................................................. 5 Magnetic orce - Qualitatie II............................................... 6 Magnetic orce - Quantitatie................................................ 7 Magnetic orce - Quantitatie II.............................................. 8 The Lorentz orce........................................................ 9 The Lorentz orce II..................................................... 10 3D World Drawn in 2D................................................... 11 Charged Particle Motion in B-ield........................................... 12 Charged Particle Motion in B-ield........................................... 13 Charged Particle Motion in B-ield II.......................................... 14 Charged Particle Motion in B-ield III......................................... 15 orce on Wires Carrying Current............................................. 16 orce on Wires Carrying Current II............................................ 17 orce on Wires Carrying Current III........................................... 18 orce on Wires Carrying Current General....................................... 19 1
Magnetic ields slide 2 0.1 Definition Magnetic ields All of us hae interacted with magnets. Motors conert electrical to mechanical energy). Computers hard dries used for data storage). Do magnets exert forces on each other? ANSWER: Yes! A great example of a magnet is a bar magnet which has poles typically called North and South. The terms north and south are arbitrary. Like poles - repel Unlike poles - attract See a resemblance to the electric field generated by point particles? PHYS102 Magnetic ields - Effects slide 2 Behaior of Poles Two north poles repel each other as shown. A north pole attracts a south pole as shown. Describe the interaction of magnets in terms of a magnetic field B) We can enision a field in much the same way we iew an E-field, but there is a ery distinct difference. E-fields can be generated by a single stationary charged particle. PHYS102 B-fields are not generated Magnetic ields - Effects slide 3 not generated by any such monopole monopole 2
What is Magnetism? so what is magnetism? magnetism is about moing electric charges! What do we know about moing charges? That s correct, the same moing electric charge we discussed when analyzing electric currents and circuits. We can calculate the force a charged particle experiences whilst in a magnetic field. PHYS102 Magnetic ields - Effects slide 4 Magnetic orce slide 5 0.2 Qualitatie Magnetic orce - Qualitatie Let s try to determine properties of the force by considering the following demonstration! A high-oltage discharge initiated in the tube creates a beam of electrons. The path of the beam is made isible when it strikes a tilted fluorescent screen. A magnetic field bar magnet) is placed near this beam. PHYS102 Magnetic ields - Effects slide 5 Magnetic orce - Qualitatie II Conclusions - from experimenting. 1. If charge is stationary in B-field, then particle experiences no magnetic force. 2. The magnetic force is always at right angles both to the elocity ) of the particle and to the B-field. 3. Magnetic force is greatest MAX) if B and is ZERO if B 4. The magnitude of the magnetic force is proportional to the charge. Summarizing the four main conclusions in one mathematical statement: B = B ) UNITS: [] = N, [] = C, [] = m/s, [B] = N s C m 1 Tesla T). PHYS102 Magnetic ields - Effects slide 6 3
Magnetic orce - Quantitatie B = B ) important note: Magnetic fields do NO Work.important note: Magnetic fields do NO Work. W = B d l = 0 Since B) d l The magnetic force magnetic force is always perpendicular perpendicular to a charged particles displacement displacement!! PHYS102 Magnetic ields - Effects slide 7 Magnetic orce - Quantitatie II B = B ) The magnitude magnitude of the magnetic force is then B B = B sin θ Where θ is the angle between the ectors and B. PHYS102 Magnetic ields - Effects slide 8 The Lorentz orce What if a charged particle is moing in an electric field and and a magnetic field? How do we describe the force acting the charged particle? Once the force acting on the charge is known, then we can use our knowledge of mechanics to sole problems! We use the superposition principle superposition principle and sum all forces acting on the charged particle. B = B ) E = E total = E + B ) total = E + B This is known as the Lorentz orce )This is known as the Lorentz orce ) PHYS102 Magnetic ields - Effects slide 9 4
The Lorentz orce II total = E + B ) It may be wise to use unit ectors use unit ectors in the aboe euation. The Lorentz force will deal with 3 dimensions uite regularly, but we draw in 2 dimensions. We need to define a notation that is consistent. PHYS102 Magnetic ields - Effects slide 10 3D World Drawn in 2D or the figure on the right, the magnetic field is perpendicular to the screen and is going into the screen. or the figure on the right, the magnetic field is perpendicular to the screen and is coming out of the screen. PHYS102 Magnetic ields - Effects slide 11 Charged Particle Motion in B-ield A positie charged particle entering a uniform magnetic field experiences a force perpendicular to its displacement. PHYS102 Magnetic ields - Effects slide 12 5
Charged Particle Motion in B-ield We could calculate the radius of curature, go back to mechanics! = m a PHYS102 B = m 2 Magnetic force responsible for centripetal Magnetic force.) ields - Effects slide 13 r r = m Charged Particle B Motion in B-ield II We could also calculate the time it takes the particle to complete one reolution. PHYS102 r = m B T = 2π r Magnetic ields - Effects slide 14 T = 2π m Called the cyclotron period.)called the cyclotron period.) B Charged Particle Motion in B-ield III rom period, we could discuss freuency. T = 2π m B f = 1 T = B 2π m PHYS102 ω = 2π f = B Magnetic ields - Effects slide 15 Called the cyclotron freuency.)called the cyclotron freuency.) m 6
orce on Wires Carrying Current If we place a current carrying wire in an external magnetic field, should the wire experience a force? We already determined an expression for the force experienced by a single charged particle moing in a magnetic field. Let s begin there: B = B We don t hae a single charged particle instead we hae a current I). PHYS102 Magnetic ields - Effects slide 16 orce on Wires Carrying Current II The magnetic force is experienced by each moing charge in the current. The total force is the product of the force on one charge with the number of charges PHYS102 B = B)nAL = I L B Magnetic ields - Effects slide 17 orce on Wires Carrying Current III B = I L B The ector L has magnitude L and is in the direction of current direction PHYS102 of current. Magnetic ields - Effects slide 18 What happens if the wire is not straight? think of 17 th -century mathematics) 7
orce on Wires Carrying Current General We begin by breaking up the wire into ery small pieces so that the length of wire is approximately straight). d B = I d s B PHYS102 B = I d s B) Magnetic ields - Effects slide 19 8