Cyclotron Motion. We can also work-out the frequency of the cyclotron motion. f cyc =
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1 Cyclotron Motion We can also work-out the frequency of the cyclotron motion f cyc = qb 2πm Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
2 Cyclotron Motion We can also work-out the frequency of the cyclotron motion f cyc = qb 2πm q/m is the particle s charge-to-mass ratio. Notice that the frequncy does not depend on the particle s velocity!! Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
3 Example Example An electron is accelerated from rest through a potential difference of 500V, the injected into a uniform magnetic field. Once in the magnetic field it completes half a revolution in 2.0ns. What is the radius of the orbit? Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
4 Example We can do the electric field part using conservation of energy: K f + qv f = K i + qv i Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
5 Example We can do the electric field part using conservation of energy: K f + qv f = K i + qv i K f + qv f = 0 + q(0) Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
6 Example We can do the electric field part using conservation of energy: K f + qv f = K i + qv i K f + qv f = 0 + q(0) 1 2 mv2 f + ( e)v f = 0 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
7 Example We can do the electric field part using conservation of energy: K f + qv f = K i + qv i K f + qv f = 0 + q(0) 1 2 mv2 f + ( e)v f = 0 v f = 2eV f m = m/s Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
8 Example We know that one orbit would take 4ns, therefore the frequency is f = 1 4ns = Hz Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
9 Example We know that one orbit would take 4ns, therefore the frequency is 1 f = 4ns = Hz f = qb 2πm Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
10 Example We know that one orbit would take 4ns, therefore the frequency is 1 f = 4ns = Hz f = qb 2πm B = 2πmf = T e The radius is then r = mv qb = 8.5mm Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
11 Example Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
12 The Cyclotron A cyclotron is useful for nuclear, particle and CM physics experiments (and creation of medical isotopes). Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
13 The Cyclotron A cyclotron is useful for nuclear, particle and CM physics experiments (and creation of medical isotopes). Exploit that the cyclotron frequency does not depend on particle velocity. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
14 The Cyclotron A cyclotron is useful for nuclear, particle and CM physics experiments (and creation of medical isotopes). Exploit that the cyclotron frequency does not depend on particle velocity. Create a powerful magnetic field and inject charged particles at the center of the device. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
15 The Cyclotron A cyclotron is useful for nuclear, particle and CM physics experiments (and creation of medical isotopes). Exploit that the cyclotron frequency does not depend on particle velocity. Create a powerful magnetic field and inject charged particles at the center of the device. Accelerate them using electric fields across gaps between the dees. Switch the sign of the potential difference at exactly the right moment to keep accelerating. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
16 The Cyclotron A cyclotron is useful for nuclear, particle and CM physics experiments (and creation of medical isotopes). Exploit that the cyclotron frequency does not depend on particle velocity. Create a powerful magnetic field and inject charged particles at the center of the device. Accelerate them using electric fields across gaps between the dees. Switch the sign of the potential difference at exactly the right moment to keep accelerating. Increase the radius until the particles escape. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
17 The World s Largest Cyclotron - TRIUMF Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
18 TRIUMF Cyclotron Tidbits First beam December 15, 1974 Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
19 TRIUMF Cyclotron Tidbits First beam December 15, m diameter magnet, about 0.6 Tesla Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
20 TRIUMF Cyclotron Tidbits First beam December 15, m diameter magnet, about 0.6 Tesla 18500A current Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
21 TRIUMF Cyclotron Tidbits First beam December 15, m diameter magnet, about 0.6 Tesla 18500A current 520MeV (particle speed is km/s) Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
22 TRIUMF Cyclotron Tidbits First beam December 15, m diameter magnet, about 0.6 Tesla 18500A current 520MeV (particle speed is km/s) accelerates 600 trillion particles (protons) per second Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
23 Magnetic Forces on Current-Carrying Wires (33.8) We have seen the effect of placing two current-carrying wires close to each other (likes attract, opposites repel). Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
24 Magnetic Forces on Current-Carrying Wires (33.8) We have seen the effect of placing two current-carrying wires close to each other (likes attract, opposites repel). Now it is time to quantify this magnetic force. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
25 Magnetic Forces on Current-Carrying Wires (33.8) We have seen the effect of placing two current-carrying wires close to each other (likes attract, opposites repel). Now it is time to quantify this magnetic force. A magnetic field parallel to a current exerts no force, perpendicular fields exert maximum force - makes sense from our knowlegde of moving charges. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
26 Magnetic Forces on Current-Carrying Wires Let s get the force in terms of current, instead of moving charges. The current in a segment of wire of length L is charge q moving through the wire divided by the time it takes t: q = I t = I L v Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
27 Magnetic Forces on Current-Carrying Wires Let s get the force in terms of current, instead of moving charges. The current in a segment of wire of length L is charge q moving through the wire divided by the time it takes t: This means that q = I t = I L v IL = qv Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
28 Magnetic Forces on Current-Carrying Wires Let s get the force in terms of current, instead of moving charges. The current in a segment of wire of length L is charge q moving through the wire divided by the time it takes t: This means that q = I t = I L v IL = qv Substituting into the force equation gives F wire = q v B = I L B Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
29 Force Between Two Parallel Wires For the specific case of two parallel wires spaced d apart, we know that the magnetic field from a long wire at distance d is B = µ 0I 2πd Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
30 Force Between Two Parallel Wires For the specific case of two parallel wires spaced d apart, we know that the magnetic field from a long wire at distance d is B = µ 0I 2πd A field of this strength is generated at the position of the second wire by the first and vice versa. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
31 Force Between Two Parallel Wires Using the right-hand-rule (and some acrobatics) you can see why opposites repel and like directions attract. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
32 Force Between Two Parallel Wires Using the right-hand-rule (and some acrobatics) you can see why opposites repel and like directions attract. The field is the same everywhere along the parallel wires. The force on the upper wire is F = I 1 LB 2 = I 1 L µ 0I 2 2πd = µ 0LI 1 I 2 2πd Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
33 Forces and Torques on Current Loops (33.9) You could see current carrying wires as repelling or attracting because of the alignment of their poles. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
34 Torque on a Current Loop Now consider a current loop in a uniform magnetic field. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
35 Torque on a Current Loop Now consider a current loop in a uniform magnetic field. In this configuration the forces on front and back cancel. However, the loop is not perpendicular to the field, so the forces on top and bottom do not cancel - there is a torque: τ = Fd = (ILB)(L sin θ) = (IL 2 )B sin θ Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
36 Torque on a Current Loop Now consider a current loop in a uniform magnetic field. In this configuration the forces on front and back cancel. However, the loop is not perpendicular to the field, so the forces on top and bottom do not cancel - there is a torque: τ = Fd = (ILB)(L sin θ) = (IL 2 )B sin θ But L 2 is the area, µ = IA so τ = µb sin θ Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
37 Torque on a Current Loop Now consider a current loop in a uniform magnetic field. In this configuration the forces on front and back cancel. However, the loop is not perpendicular to the field, so the forces on top and bottom do not cancel - there is a torque: τ = Fd = (ILB)(L sin θ) = (IL 2 )B sin θ But L 2 is the area, µ = IA so τ = µb sin θ Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
38 Torque on a Current Loop Now consider a current loop in a uniform magnetic field. In this configuration the forces on front and back cancel. However, the loop is not perpendicular to the field, so the forces on top and bottom do not cancel - there is a torque: τ = Fd = (ILB)(L sin θ) = (IL 2 )B sin θ But L 2 is the area, µ = IA so τ = µb sin θ τ = µ B Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
39 An Electric Motor Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 1
The Direction of Magnetic Field. Neil Alberding (SFU Physics) Physics 121: Optics, Electricity & Magnetism Spring / 16
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