Consider the situation for which B is not uniform.
r=mv/qB
Strong B
weak B
Strong B
Figure 1
This situation called particle trapped in a Magnetic Bottle.
Earth Magnetic field protect the earth from charged particles coming from the outer space.
In the day time a large number of charged particles come towards the earth. But most of the do not reach
the earth.
They get trapped in the magnetic field of the earth.
Particle moves
like Helix
Figure 2
The aurora borealis or the northern lights in Sweden
The aurora australis or the southern lights in Antarctica
These particles ionized the atmosphere gases near the poles.
Those ionized or excited gases emit photons when they returning from an excited state to ground state.
This creates a light that called Auroras.
Using observation made on F, we formulated a vector quantity B which can be used to characterize each
and every point in the magnetic field (like E).
B is analogous to E
Path of a charged particle in a region with a magnetic field (B) and an electric field
(E)
Let us assume E is perpendicular to B
V
F=qV
B
F=qE
V
qBV
qE
Figure 3
If these two forces are equal, then the particle moves without being deviated.
qBV=Eq
V=E/B
If we send a beam of charged particles having different velocities, only those having velocity=E/B travel
without being deviated.
Charged
Particle Beam
Figure 4
A device which can produce charged particles with same velocity using this method is called a SELECTOR.
Mass spectrometer
This equipment is used to
1. Separate out isotopes of an element in form of ions.
2. To determine the mss of a charged particles (ions).
A beam of charged particles is obtained from a source.
The charged particles are accelerated by using potential field.
This beam is passed through a selector and set of charged particles with same velocity is obtained (V).
These charged particles are passed through a region of constant magnetic field, normal to the field.
Photographic
Plate
d
m2
m1
Figure 5
Charged particles move in a circular path
r=mV/qB
d/2=mEs/qBBs
Where Bs is the selector magnetic field
d=2mEs/qBBs
Assume that, there were two isotopes in the beam with mass m1 and m2.
d1=2m1Es/qBBs
d2=2m2Es/qBBs
Since d1 and d2 can be measured.
If m1 is known then m2 can be calculated.
Since particle with different masses going in circles of different diameters, they can be collected easily.
Accelerate the stationary charged particles
V
V=Potential
v=velocity
Figure 6
Using law of conservation of energy
mv2/2-qV=0
potential energy at B is –V
v=√(2qV/m)
This called Linear accelerator
Linear accelerators are very long. There is a Linear accelerator in MIT (Massachusetts Institute of
Technology) that is 2 miles long.
Cyclotron
Cyclotron is a type of particle accelerator. (Accelerator is a device that can be used to give charged particles
to very high energy or speed)
In high energy or particle physics some fundamental particles are given very high velocities and allow them
to collide.
New particles that are generated as a result of these collisions.
The Noble prizes in physics for 1976 and 1984 were awarded for just such studies.
The first Cyclotron was manufactured by Ernest Lawrence, of the University of California, Berkeley (1932).
Hall experiment
Until 1879, it was believed that electric current are due to the movement of positive (+) charges. In 1879
Edwin H. Hall conducted an experiment to illustrate that electric current are due to the movement of
negative (-) charges.
A copper strip was placed normal to a magnetic field and a current was passed through it.
Case 1
Case 2
Figure 7
Due to
, positive charges will move
towards Top edge, giving higher potential
to Top edge compare to Bottom edge.
Due to
, negative charges will move
towards Bottom edge, this gives higher potential
to Bottom edge compare to Top edge.
By connecting a voltmeter across the width, we can measure the potential difference between the two
edges.
Voltmeter can tell us which edge is at higher potential.
Experimental result was tally with case 2.
Therefore it was concluded that an electric current is due to the motion of negative charges.
But electron discovered in 1879 by J.J. Thomson.
As time goes on, electric field of edges balance with
, called Hall Potential.
Then if we increase the current, there is no effect on Hall potential.
qE=qVdB
but
Vd=i/neA
E=iB/neA
n=iB/eEA
and E=V/d
Where d=strip width
n=iB/Vle
where l=thickness of the strip
Force acting on a current carrying conductor in magnetic field
Figure 8
Where n-number of negative charges per unit volume.
Force acting on an electron=-e(VdxB)
=eVdBsinθ
Total force acting on all electrons (on the conductor)=(eVdBsinθ)(Aln)
=(eVdBsinθ)(Al)(i/eAVd)
=Bilsinθ
If θ=90 then F=Bil
We can represent l using a vector that has magnitude l and direction is same as that of the current.
F=ilxB
Force acting on a wire which is not straight, that is in a magnetic field.
C
Figure 9
F=sum df=idlxB through curve C
Torque acting on a Rectangular current carrying loop
FAB
FBC
+
+
+
+ FAB
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
FAD
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Fcd +
+
+
b
FCD
Figure 10
ABCD is a rectangular coil.
We can easily see that Fad and Fcb are equal and opposite, and also acting along the same line.
Fab=ilxB
=ilB
Fdc= ilxB
=ilB
These two forces will form a couple
Torque=(BIl)(bsinθ)
=Bi(lb) sinθ
=BiAsinθ
If there are N turns
Torque (τ)=NiBAsinθ