Cyclotron, final. The cyclotron s operation is based on the fact that T is independent of the speed of the particles and of the radius of their path

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1 Cyclotron, final The cyclotron s operation is based on the fact that T is independent of the speed of the particles and of the radius of their path K 1 qbr 2 2m 2 = mv = When the energy of the ions in a cyclotron exceeds about 20 MeV, relativistic effects come into play

2 Cyclotron, 2 D 1 and D 2 are called dees because of their shape A high frequency alternating potential is applied to the dees A uniform magnetic field is perpendicular to them

3 Hall Effect When a current carrying conductor is placed in a magnetic field, a potential difference is generated in a direction perpendicular to both the current and the magnetic field This phenomena is known as the Hall effect It arises from the deflection of charge carriers to one side of the conductor as a result of the magnetic forces they experience

4 Hall Voltage This shows an arrangement for observing the Hall effect The Hall voltage is measured between points a and c

5 Hall Voltage, final ΔV H = E H d = v d B d V d is the width of the conductor v d is the drift velocity If B and d are known, v d can be found I B RH I B Δ H = = nqt t R H = 1 / nq is called the Hall coefficient A properly calibrated conductor can be used to measure the magnitude of an unknown magnetic field

6 Quick Quiz 29.4 The four wires shown below all carry the same current from point A to point B through the same magnetic field. In all four parts of the figure, the points A and B are 10 cm apart. Which of the following ranks wires according to the magnitude of the magnetic force exerted on them, from greatest to least? (a) b, c, d (b) a, c, b (c) d, c, b (d) c, a, b (e) No force is exerted on any of the wires.

7 Quick Quiz 29.4 Answer: (a). (a), (b) = (c), (d). The magnitude of the force depends on the value of sin θ. The maximum force occurs when the wire is perpendicular to the field (a), and there is zero force when the wire is parallel (d). Choices (b) and (c) represent the same force because Case 1 tells us that a straight wire between A and B will have the same force on it as the curved wire.

8 Quick Quiz 29.6 Rank the magnitudes of the torques acting on the rectangular loops shown in the figure below, from highest to lowest. (All the loops are identical and carry the same current.) (a) a, b, c (b) b, c, a (c) c, b, a (d) a, c, b. (e) All loops experience zero torque.

9 Quick Quiz 29.7 Rank the magnitudes of the net forces acting on the rectangular loops shown in this figure, from highest to lowest. (All the loops are identical and carry the same current.) (a) a, b, c (b) b, c, a (c) c, b, a (d) b, a, c (e) All loops experience zero net force.

10 Quick Quiz 29.10a Three types of particles enter a mass spectrometer like the one shown in your book as Figure The figure below shows where the particles strike the detector array. Rank the particles that arrive at a, b, and c by speed. (a) a, b, c (b) b, c, a (c) c, b, a (d) All their speeds are equal.

11 Quick Quiz 29.10a Answer: (d). The velocity selector ensures that all three types of particles have the same speed.

12 Quick Quiz 29.10b Rank the particles that arrive at a, b, and c by m/q ratio. (a) a, b, c (b) b, c, a (c) c, b, a (d) All their m/q ratios are equal.

13 Chapter 30 Sources of the Magnetic Field

14 Biot-Savart Law Introduction Biot and Savart conducted experiments on the force exerted by an electric current on a nearby magnet They arrived at a mathematical expression that gives the magnetic field at some point in space due to a current

15 Biot-Savart Law Set-Up The magnetic field is db at some point P The length element is ds The wire is carrying a steady current of I

16 Biot-Savart Law Observations The vector db is perpendicular to both ds and to the unit vector rˆ directed from ds toward P The magnitude of db is inversely proportional to r 2, where r is the distance from ds to P

17 Biot-Savart Law Observations, cont The magnitude of db is proportional to the current and to the magnitude ds of the length element ds The magnitude of db is proportional to sin θ, where θ is the angle between the vectors ds and rˆ

18 Biot-Savart Law Equation The observations are summarized in the mathematical equation called the Biot- Savart law: db = μo 4π I ds ˆr 2 r The magnetic field described by the law is the field due to the current-carrying conductor

19 Permeability of Free Space The constant μ o is called the permeability of free space μ o = 4π x 10-7 T. m / A

20 Total Magnetic Field db is the field created by the current in the length segment ds To find the total field, sum up the contributions from all the current elements I ds μ ˆ o I d B = s r 2 4π r The integral is over the entire current distribution

21 B for a Long, Straight Conductor The thin, straight wire is carrying a constant current ˆ sin ds r = dx θ ( ) Integrating over all the current elements gives μ I θ2 o B = sinθ dθ 4πa θ1 μo I = 4πa ( cosθ cosθ ) 1 2 kˆ

22 B for a Long, Straight Conductor, Special Case If the conductor is an infinitely long, straight wire, θ 1 = 0 and θ 2 = π The field becomes μ I B = o 2πa

23 B for a Long, Straight Conductor, Direction The magnetic field lines are circles concentric with the wire The field lines lie in planes perpendicular to to wire The magnitude of B is constant on any circle of radius a The right-hand rule for determining the direction of B is shown

24 B for a Circular Current Loop The loop has a radius of R and carries a steady current of I Find B at point P B x = 2 μ I R 2 o ( x + R )

Today s lecture: Motion in a Uniform Magnetic Field continued Force on a Current Carrying Conductor Introduction to the Biot-Savart Law

PHYSICS 1B Today s lecture: Motion in a Uniform Magnetic Field continued Force on a Current Carrying Conductor Introduction to the Biot-Savart Law Electricity & Magnetism A Charged Particle in a Magnetic