Thomson’s parabola method | EMFT and Relativity | Motion of charged particles in E and B fields

Thomson’s parabola method

Positive ray analysis

• This method is used to find the charge to mass ratio.

Thomson parabola method

• T = Discharge tube, the pressure of gas in this tube is kept 0.01 mm of Hg
• E = Capillary tube
• C = Cathode, which is perforated with an extremely small holes
• W = Water jacket, used to cool the cathode
• A and B = Metallic plates, the electric field is applied between these plates
• N and S = North and south poles of a heavy magnet
• K = Highly evacuated camera
• P = Photographic plate
• R = Liquid air trap, used to keep the pressure in K quite low

Working

• To ensure the supply of the gas, a steady steam of the gas is allowed to pass through E and after circulating the tube, it is escaped through M.
• The positive ion produced in T move towards C.
• The ion which reaches C axially. pass through its fine hole in the form of narrow beam.
• After crossing C, the parallel beam of ions enters into the electric and magnetic field.
• The electric field is perpendicular to the direction of ions.
• After it the beam enters into K and finally it is received on P.
• When the photographic plate P is exposed, we get a series of parabolas.

Theory

• Let m, q and v are mass, charge and velocity of positive ions respectively.
• When no field is applied, then these ions will strike at point O.
• Here O is undeflected spot.

Action of electric field (E)

• Let l = length of path of positive ions over which the electric field is applied.
• Force on particle due to electric field E, F_e = qE
• Now, acceleration on particle, a = qE / m
• Time taken by particle to cross electric field, t = l / v
• Since u = 0, and a = qE / m, therefore
• Displacement of particle

• After crossing E, the ion moves in a straight line, and strikes at a point on photographic plate, which is at a distance x from O

Action of magnetic field (B)

• Let the magnetic field B is applied in the same direction as E and over the same length l.
• Due to magnetic field, the positive ions will deflect, but their deflection will be at right angle to the deflection of ions due to electric field.
• Let due to B, the positive ions strikes the plate at a distance y from O, and OY ⊥ OX.

                F_m = qvB

    ∵        a՛ = F_m / m

    ∴        a՛ = qvB / m

• Displacement

Action of combined electric (E) and magnetic field (B)

• For it we eliminate v from x and y.

• If E and B are kept at a constant value, and if q/m is constant, then

• This is equation of parabola. It means the motion of a charged particle in electromagnetic field will be parabolic in nature.
• Since the equation of y² / x is independent of v, so the particle of same q/m, but of different v will fall on the different points of same parabola.

• The position of any individual particle will depend on v.
• The entire parabola is a velocity dispersion or a velocity spectrum.
• Since this equation depends on q/m, so the ions of different q/m will lie along the different parabola.

To know more about Thomson parabola method please click on the link https://youtu.be/2pLO0N_MNHk