Question

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particles has the highest charge to mass ratio ?

(a) Suppose two particles have identical curved trajectories true ?
(i) they have same charge (ii), they have same charge mass (iii) the charges have the same sign. (iv) they have the same `e//m` ration.
(b) you are given the initial velocity v of a beam particale and the length of the capacitor l. What other measurement would enable one to find `e//m ?`

Answer 1

The charge on particles `1 and 2` , must be negative and charge on particle `3` must be positive. We shall show that charge to mass ration `(e//m)` is highest in case of particale `3`.
If we assume that the three charged particles have enetered the electric field with the same velocity, then the deflection is proportional to `(e//m)` of this particale must be the highest.
(a) When two particles have identical curved trajectories, their charges must have the same sign and the particles must have the same `e//m` ration.
(b) if h is the vertical displacement of particle at the end of capacitor plates as shown in Figure then, from

`s = ut + (1)/(2) at^(2)`
`h = 0 + (1)/(2) ((eE)/(m)) ((l)/(v))^(2) = (1)/(2) ((e)/(m)) (El^(2))/(v^(2))`
`e//m = (2v^(2)h)/(E l^(2))`
As E, l and v are known, by measuring h, we can calculate `(e//m)`.
The relation shws that for given `E, l and v ,` deflection `(h) prop (e//m)`. This is what we have stated above.