Question

An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle α with the plates. It leaves the plates at angle β with kinetic energy K2. Then the ratio of kinetic energy K1 to K2 will be:

(a) tan(α)/tan(β)
(b) tan(β)/tan(α)
(c) cos(α)/cos(β)
(d) sin(α)/sin(β)

Answer 1

The ratio of kinetic energy K1 to K2 can be determined using the conservation of energy. Initially, the electron has kinetic energy K1 and final kinetic energy K2. The ratio is given by K1/K2 = 1 + qV/K2, where q is the charge of the electron and V is the potential difference between the plates.

Step-by-step explanation:

The ratio of kinetic energy K1 to K2 can be determined using the conservation of energy. The change in kinetic energy of the electron between the plates is equal to the work done on it by the electric field. Initially, the electron has kinetic energy K1 and final kinetic energy K2. Let's denote the charge of the electron as q, the electric field between the plates as E, the potential difference as V, and the distance between the plates as d.

Initially, the electron has no potential energy, so the initial total energy is given by:

E_initial = K1 + 0 = K1

Finally, the electron has potential energy due to the electric field, so the final total energy is given by:

E_final = 0 + qV = qV

Since the total energy is conserved, we have:

K1 = K2 + qV

Therefore, the ratio of kinetic energy K1 to K2 is:

K1/K2 = (K2 + qV)/K2

Simplifying this expression, we get:

K1/K2 = 1 + qV/K2

As you can see, the ratio of K1 to K2 depends on the potential difference V and the charge q of the electron.