## Motion of Charged Particle Through Magnetic Field

♦ Study about the Motion of Charged Particle Through Magnetic Field . The path of the particle in the magnetic field is circular ♦

The magnetic force equation gives, for a particle of charge q , mass m , velocity u, magnetic field B ,

The radius of the circular path is

Note : The figure shows a charged particle , moving in a Straight line , enters a region of magnetic field (field upwards). Once the particle is inside the field region, it experiences a magnetic force qvB . The path of the particle in the magnetic field is circular. Once it leaves the field region, the path becomes a straight line again. Let a screen is placed at a distance D from the centre of the field region. Then, the displacement OP’ , is X = D tanθ . It can be proved that tanθ = qBL/mu

Notice the difference, that when particle crosses a perpendicular electric field region, and hits the screen, the displacement observed is Y = qELD/mu2 while when it crosses a perpendicular magnetic field region and hits the screen, the displacement is X = qBLD/mu.

## Motion of Charged Particle Through Electric Field

♦ Study about the Motion of Charged Particle Through Electric Field . The path of the particle in the Electric  field is parabolic  ♦

Consider a particle of mass m , charge q , moving horizontally with velocity u , as shown in the figure. The charge enters a region between two parallel plates (length L), where an electric field E , as shown exists. Since, there is no horizontal force on the particle , the horizontal component of velocity does not change ,
vx = u at all times . The time spent by the particle in the field region is

t = L/u

During this time, the particle experiences a vertical force Fy = qE . Due to this force acceleration in
Y-direction is ay = qE/m . In time t , the velocity acquired in Y-direction is

vy = ayt

vy = qEL/mu

The angle θ , at which the particle emerges out of the field (figure) is

tan θ = vy/vx

The velocity with which the particle comes out of the field is

The path of the particle in this case is parabolic this can be seen as follows. In any time t, the distances traveled by the particle in x, and y direction are

eliminating t , we get

y ∝ x2

The path is a parabola.

## Photo Electric Effect & Laws of Photo Electric Effect

♦ Learn about : Photo Electric Effect : LENARD’S EXPLANATION , EXPERIMENTAL ARRANGEMENT ♦

• Hertz observed that when ultra violet rays are allowed to fall on negative plate of an electric discharge tube, then conduction takes place more easily. This shows that electrons are ejected from a metal surface when illuminated by light of suitable wavelength .
• After some time, Hall wach confirmed above observation through his following convincing experiment : His apparatus consists of two zinc plates enclosed in an evacuated quartz tube.

The plates are connected to a battery through a galvanometer (fig.). He noted following observations :

• When U.V. rays are allowed to fall on the cathode, deflection is produced in the galvanometer i.e., a current flows in the circuit.
• As soon as rays are stopped, the deflection in the galvanometer becomes zero or current stops.
• If rays are made to fall on anode then either no current or a very small current flows in the circuit.

LENARD’S EXPLANATION :

(a) He told that when ultraviolet rays fall on cathode electrons are ejected from it which are attracted toward anode or positively charged plate. Hence, the circuit which was incomplete till now, due to air gap between two plates in the tube, gets completed due to flow of electrons and a current starts flowing in the circuit.

• However, when rays fall on anode, the electrons are again emitted from the plate in the same way as earlier but because of being negatively charged do not reach the cathode i.e., circuit again remains incomplete and the current does not flow.

This phenomenon of emission of electrons from a metallic surface when illuminated by light of appropriate wavelength frequency is known as PHOTO ELECTRIC EFFECT. The electrons emitted in this process are called as photo-electrons and the current produced in the circuit is called as photo-electric current.

#### Note :-

• Photo-electric effect is a general phenomenon exhibited by all substances when illuminated by radiations of suitable wavelength. This suitable wavelength is different for substances.
• Certain alkali-metals e.g. Sodium, Potassium, Calcium etc., show the photo electric effect when visible light (l = 4000 Aº − 7500 Aº) falls on them.
###### EXPERIMENTAL ARRANGEMENT :

Study of the dependence of maximum kinetic energy and photo electric current.

###### ♦ Learn about : Laws of Photo Electric Effect : Intensity effect , Frequency effect , Effect of nature of metals , Time-delay effect ♦

(a)Intensity effect : For a given metal, rate of emission of photo-electrons i.e., photo current is directly proportional to the intensity of incident radiation for a given light i.e., bright light always gives more photo-current than a dim one for a given frequency.

(b)Frequency effect : For a given metal, maximum kinetic energy of photo electrons varies linearly with the frequency of incident radiation and is independent of its intensity i.e., blue light will always give more energetic photoelectrons than red, whatever be its intensity.

(c) Effect of nature of metals : If light of different frequencies in turn is incident on a given metal, photo electric effect takes place only if the frequency of incident radiation is more ( or wavelength is less ) than a specific value V0 . This specific value of frequency (V0) is called threshold-frequency or cut-off frequency and depends only on the nature of metal.

So if from a certain metal, green light can emit photo electrons while yellow can not, blue light will emit photo electrons (as VB>VG) while red will not. For PEE ν ≥ ν­0   , λ ≤ λ­0

(d) Time-delay effect : Within the limits of experimental accuracy (about 10–9 s.), there is no time lag between incidence of radiation and emission of photo electrons i.e., as light is incident on the metal photo electrons are emitted.

(e) The rate at which the electrons are emitted from a photocathode is independent of its temperature. This shows that it is different from thermionic emission.

Note : –

• In accordance with conservation of energy photo electric effect represents conversion of light energy reverse of what happens in an electric bulb.
• Photo electric effect takes place only if the electron is loosely bound to the metal, i.e., photo-electric effect can never take place with completely free electron.
• In photo-electric effect all the emitted photo electrons do not have same kinetic energy. The emitted photo electrons have kinetic energy in the range from 0 to a maximum value. Kmax depends both on frequency of incident radiation and nature of metal.
• With emission of photo electrons the metal will become positively charged and if isolated, photoelectric effect will cease after some time when potential acquired by the metal V is such that eV = Kmax. in this situation any electron emitted by the metal will turn back to it by attractive force and will not escape.
• The opposite of photo-electric effect i.e. emission of electromagnetic radiation. From a metal when electrons strikes it results in the production of X-rays and is called ‘inverse photo electric effect.
• Apart from photo electric emission, electrons can also be emitted from a metal by heating (Thermionic – emission), by applying a strong electric field (field emission) or by bombarding it with electrons (secondary emission).
• Irradiation of a substance by light under specific conditions instead of producing photoelectric effect may increase its electrical conductivity resulting in ‘photo conductive effect’ or may produce an EMF across it resulting in photo Voltaic effect.

## Diamagnetic , Paramagnetic & Ferromagnetic substance

Diamagnetic substance: Diamagnetic substances are those substances which are repelled by a magnet. From microscopic point of view, these are the substances whose atomic orbitals are completely filled. The cause of magnetization for these substances is the orbital motion of electron in which velocity of the electron is affected by the external magnetic field. Some examples of diamagnetic substances are antimony, bismuth, copper, lead, gold, silver, zinc, quartz, mercury, alcohol, sodium chloride, water, hydrogen, air, argon etc.

Properties of diamagnetic substances:

(1)  When placed in a non-uniform magnetic field, it tends to move from stronger to weaker regions of the magnetic field. For example, when a diamagnetic liquid in a watch glass is placed on two pole pieces lying close to each other, we observe a depression in the middle and when the pole pieces are placed sufficiently apart, then we observe depressions at the sides .

(2)  A diamagnetic rod when placed in a uniform magnetic field, the rod aligns itself in a direction perpendicular to the direction of the magnetic field.

(3)  The permeability of a diamagnetic substance is less than one.

(4)  When it is placed in a magnetic field, it develops weak magnetization in a direction opposite to the direction of the magnetizing field.

(5)  As soon as the magnetizing field is removed, it loses its magnetization.

(6)  The magnetic susceptibility does not depend upon temperature. It has a small negative value.

### Paramagnetic substance:

Paramagnetic substances are the substances which are feebly attracted by a magnet. The atomic orbitals of these substances are partially filled and hence there exists unpaired electrons the cause of magnetisation for these materials is spin and orbital motion of electrons. Some examples include aluminium, chromium, manganese, oxygen, platinum, alkali and alkaline earth metals.
Properties of paramagnetic substances:

(1)  Removing the magnetizing field, the paramagnetics lose their magnetisation.

(2)  It develops weak magnetisation along the direction of magnetic field.

(3)  The magnetic lines of force prefer to pass through the material.

(4)  When suspended freely in a uniform magnetic field, it aligns itself in the direction of  magnetic field.

(5)  It moves from weaker to stronger parts of the magnetic field.

(6)  The magnetic permeability is slightly greater than one.

### Ferromagnetic substances:

These are the substances which are strongly attracted by a magnet  and can be magnetised. Ferromagnetic substances are paramagnetic in nature lent their behaviour is much more intense. Ferromagnetism can be explained on the basis of domain theory. The cause of magnetisation for these substances is the formation of domains.

(i)   Domain is a region in which magnetic moment of all atoms is in the same direction.

(ii)  At normal temperatures these domains are distributed randomly throughout the entire material. Hence net magnetic moment of the substance is zero.

Some examples of ferromagnetic substances are iron, cobalt, nickel, gadolinium, dysprosium etc.

Properties of ferromagnetic substances

(1)  When placed in a non-uniform magnetic field, it moves from weaker to stronger parts of the magnetic field. For example, when a ferromagnetic liquid in a watch glass is placed on two closely placed pole pieces, it is observed that the liquid moves the side to the middle and when the pole pieces are moved apart, the liquid gets depressed in the middle.

(2)  The magnetic lines of force tend to pass through the material.

(3)  When suspended freely in a uniform magnetic field, it aligns itself parallel to the direction of the magnetic field.

(4)  When it is placed in a magnetic field, it develops strong induced magnetism.

(5)  With the removal of the magnetizing field, it does not lose its magnetisation.

(6)  Its permeability is extremely large compared to that of free space. Hence B >> H.

(7)  Magnetic susceptibility has a very large positive value.

(8)  When placed in a magnetic field, it is strongly magnetized in the direction of the magnetic field.

(9)  The magnetic susceptibility decreases with increase of temperature. That’s why the ferromagnetism decreases with rise of temperature. Maximum at absolute zero of temperature and drops to zero at Curie temperature.

## Cathode Rays & Positive Rays

Cathode rays are streams of fast moving electrons.

Properties : (i) Cathode rays are emitted normally from the cathode surface. Their direction is independent of the position of the anode.

(ii) Cathode rays travel in straight lines. (Cast shadows of objects placed in their path).

(iii) Cathode rays exert mechanical force on the objects they strike.

(iv) Cathode rays produce heat when they strike a material surface.

(v) Cathode rays produce fluorescence when they strike a number of crystals, minerals and slats.

(vi) When cathode ray strike a solid object, specially a metal, X-rays are emitted from the object. (It is not safe to use Geissler tube at potential differences above about 5–6 kV because of this X-ray emission, generated by striking of cathode rays of metal anode).

(vii) Cathode rays are deflected by an electric field and also by a magnetic field. The direction of deflection is the same as that of a stream of negatively charged particles.

(viii) Cathode rays ionize the gas through which they are passed.

(ix) Cathode rays can penetrate thin foils of metal.

(x) Cathode rays affect photographic plates.

(xi) Cathode rays are found to have velocity upto one tenth of the velocity of light. The e/m of electrons was measured by J.J. Thomson (so credit of discovering electron is given to Thomson).

The e of electron was measured by R.A./Millikan e/m = 1.759 x 1011 c/kg e = 1.602 x 10–19 C m = 9.09 x 10–31 kg

The e/m of an electron is called the specific charge of an electron.

If one includes the relativistic variation of mass with speed then specific charge of an electron decreases with the increase in the velocity of the electron.

## Positive Rays :

Positive rays are sometimes known as the canal rays. These were discovered in 1896 by Goldstein. If the cathode of a discharge tube has holes in it and the pressure of the gas is around 1 mm of mercury than faint luminous glow come out from each hole on the backside of the cathode.

This shows that something is coming out of the holes. These are called canal rays or positive rays.

## Origin of positive rays :

When potential difference is applied across the electrodes, electrons (cathode rays) are emitted from the cathode. As they move towards anode, they gain energy.

These energetic electrons which collide with the atoms of the gas in the discharge tube, they ionize the atoms. The positive ions formed at various places between cathode and anode, travel towards the cathode. Since during their motion, the positive ions when reach the cathode, some pass through the holes in the cathode. These stream of positive ions are the positive rays or canal rays.

If the discharge tube is totally evacuated then no positive rays are produced. Thus positive rays are positive ions of the gas in the tube. Properties of positive rays were studied by Thomson. The q/m of the hydrogen was found to be ~108 C/kg much less then the e/m of electron ~1011 C/kg indicating that mass of positive rays is much greater than that of electrons.

## Properties of Positive Rays :

(i) These are positive ions having same mass if the experimental gas does not have isotopes. However if the gas has isotopes then positive rays are group of positive ions having different masses.

(ii) They travel in straight lines and cast shadows of objects placed in their path. But the speed of the positive rays is much smaller than that of cathode rays.

(iii) They are deflected by electric and magnetic fields but the deflections are small as compared to that of cathode rays.

(iv) They show a spectrum of velocities. Different positive ions move with different velocities.

(v) q/m ratio of these rays depends on the nature of the gas in the tube (while in case of the cathode rays q/m is constant and does not depend on the gas in the tube).

(vi) They carry energy and momentum.

(vii) They cause ionization (which is much more than that produced by cathode rays).

(viii) They cause fluorescence (in ZnS or CdS screen) and affect photographic plates.

(ix) They have a little penetration power (but much less in comparison to cathode rays)