general physics ii, lec 16, by/ t.a. eleyan 1 lecture 16 magnetic fields& force

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

1

Lecture 16Magnetic Fields& Force


2

Torque on a Current LoopImagine a current loop in a magnetic field as follows:

1 2F F BIb

BI

b

a

Ba/2

F

F

F

F

max BIba BIA

sinBIA

In a motor, one has “N” loops of current


3

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.

B

30.0o


4

GalvanometerDevice used in the construction of ammeters and voltmeters.


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

Rp


6

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

Rs


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.


8

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


9

Example : Proton moving in uniform magnetic fieldA 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.


10

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 x

x x

m

qBf

2

kg

TCf

27

19

1067.12

4.0106.1

HzHzf 68 101.61067.128.6

4.06.1

Hzf 6101.6

m

qBrv

kg

mTCv

27

19

1067.1

21.04.0106.1

s

m

s

mv 68 101.81067.1

21.04.06.1

s

mv 6101.8


11

[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 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m=2.18×10-26 kg.


12

Example: Mass Spectrometer

Suppose that B=80mT, V=1000V. A charged ion (1.6022 10-19C) 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.


13


14

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


15

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


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=3.34 10-27kg)?


17

ExampleSuppose 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=3.34 10-27kg, B=1.57

T)?

A) 0.9 10-14 J

B) 8.47 10-13 J C) 2.7 10-12 J

D) 3.74 10-13 JJ 107.2

m/s 1099.3 implies

12221

7

mvK

mRqB

vqBmv

r

general physics ii, lec 16, by/ t.a. eleyan 1 lecture 16 magnetic fields& force

Documents

ogeneral physics

frequencygeneral physics

eleyangeneral physics

magnetic fieldconsider

uniform magnetic fielda

b field

circular loop of radius

eleyanthe magnetic force