1. Lecture 16 Magnetic Fields& Force
General Physics II, Lec 16, By/ T.A. Eleyan

2. Torque on a Current Loop
Imagine a current loop in a magnetic field as follows: B I b a
a/2 F
In a motor, one has “N” loops of current
General Physics II, Lec 16, By/ T.A. Eleyan

3. General Physics II, Lec 16, By/ T.A. Eleyan
Example:
A circular loop of radius 50.0 cm is oriented at an angle of 30.0o to a magnetic field of 0.50 T. The current in the loop is 2.0 A. Find the magnitude of the torque.
30.0o B
General Physics II, Lec 16, By/ T.A. Eleyan

4. General Physics II, Lec 16, By/ T.A. Eleyan
Galvanometer
Device used in the construction of ammeters and voltmeters.
General Physics II, Lec 16, By/ T.A. Eleyan

5. Galvanometer used as Ammeter
Typical galvanometer have an internal resistance of the order of 60 W - that could significantly disturb (reduce) a current measurement.
Built to have full scale for small current ~ 1 mA or less.
Must therefore be mounted in parallel with a small resistor or shunt resistor.
Galvanometer
60 W Rp
General Physics II, Lec 16, By/ T.A. Eleyan

6. General Physics II, Lec 16, By/ T.A. Eleyan
Galvanometer used as Voltmeter
Finite internal resistance of a galvanometer must also addressed if one wishes to use it as voltmeter.
Must mounted a large resistor in series to limit the current going though the voltmeter to 1 mA.
Must also have a large resistance to avoid disturbing circuit when measured in parallel.
Galvanometer
60 W Rs
General Physics II, Lec 16, By/ T.A. Eleyan

7. Motion of Charged Particle in magnetic field
Consider positively charge particle moving in a uniform magnetic field.
Suppose the initial velocity of the particle is perpendicular to the direction of the field.
Then a magnetic force will be exerted on the particle and make follow a circular path.
General Physics II, Lec 16, By/ T.A. Eleyan

8. General Physics II, Lec 16, By/ T.A. Eleyan
The magnetic force produces a centripetal acceleration.
The particle travels on a circular trajectory with a radius:
What is the period of revolution of the motion?
The frequency
General Physics II, Lec 16, By/ T.A. Eleyan

9. Example : Proton moving in uniform magnetic field
A proton is moving in a circular orbit of radius 14 cm in a uniform magnetic field of magnitude 0.35 T, directed perpendicular to the velocity of the proton. Find the orbital speed of the proton.
General Physics II, Lec 16, By/ T.A. Eleyan

10. General Physics II, Lec 16, By/ T.A. Eleyan
Example: If a proton moves in a circle of radius 21 cm perpendicular to a B field of 0.4 T, what is the speed of the proton and the frequency of motion? v r x
General Physics II, Lec 16, By/ T.A. Eleyan

11. General Physics II, Lec 16, By/ T.A. Eleyan
[Q]: Consider the mass spectrometer. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of T. Calculate the radius of the path in the system for a singly charged ion with mass m=2.18×10-26 kg.
General Physics II, Lec 16, By/ T.A. Eleyan

12. Example: Mass Spectrometer
Suppose that B=80mT, V=1000V. A charged ion ( C) enters the chamber and strikes the detector at a distance x=1.6254m. What is the mass of the ion?
Key Idea: The uniform magnetic field forces the ion on a circular path and the ion’s mass can be related to the radius of the circular trajectory.
General Physics II, Lec 16, By/ T.A. Eleyan

13. General Physics II, Lec 16, By/ T.A. Eleyan

14. General Physics II, Lec 16, By/ T.A. Eleyan
Cyclotrons
A cyclotron is a particle accelerator
The D-shaped pieces (descriptively called “dees”) have alternating electric potentials applied to them such that a positively charged particle always sees a negatively charged dee ahead when it emerges from under the previous dee, which is now positively charged
General Physics II, Lec 16, By/ T.A. Eleyan

15. General Physics II, Lec 16, By/ T.A. Eleyan
The resulting electric field accelerates the particle
Because the cyclotron sits in a strong magnetic field, the trajectory is curved
The radius of the trajectory is proportional to the momentum, so the accelerated particle spirals outward
General Physics II, Lec 16, By/ T.A. Eleyan

16. Example: Deuteron in Cyclotron
Suppose a cyclotron is operated at frequency f=12 MHz and has a dee radius of R=53cm. What is the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron (m= kg)?
General Physics II, Lec 16, By/ T.A. Eleyan

17. General Physics II, Lec 16, By/ T.A. Eleyan
Example
Suppose a cyclotron is operated at frequency f=12 MHz and has a dee radius of R=53cm. What is the kinetic energy of the deuterons in this cyclotron when they travel on a circular trajectory with radius R (m= kg, B=1.57 T)?
A) J
B) J
C) J
D) J
General Physics II, Lec 16, By/ T.A. Eleyan