Two oppositely-charged parallel metal plates are situated in a vacuum, as shown in Fig. Plates have length L.

Q#386: [Electricity > Electric field] (Past Exam Paper – November 2010 Paper 23 Q7)

Two oppositely-charged parallel metal plates are situated in a vacuum, as shown in Fig.

Plates have length L.

Uniform electric field between plates has magnitude E. Electric field outside plates is zero.

Positively-charged particle has mass m and charge +q. Before particle reaches the region between the plates, it is travelling with speed v parallel to the plates.

Particle passes between plates and into the region beyond them.

(a)

(i) On Fig, draw path of the particle between the plates and beyond them.

(ii) For the particle in region between the plates, state expressions, in terms of E, m, q, v and L, as appropriate, for

1. Force F on the particle

2. time t for particle to cross the region between the plates

(b)

(i) State law of conservation of linear momentum.

(ii) Use answers in (a)(ii) to state an expression for change in momentum of the particle.

(iii) Suggest and explain whether law of conservation of linear momentum applies to the particle moving between the plates.

Solution 386:

(a)

(i) The path is a reasonable curve upwards between plates and straight and at a tangent to the curve beyond the plates

(ii)

1. Force F = Eq

2. {The force F only causes an acceleration vertically, it does not affect the horizontal motion.}

Time t = L / v

(b)

(i) The law of conservation of momentum states that the total momentum of a system remains constant OR the total momentum of a system before a collision equals the total momentum after collision

provided no external force acts on the system.

(ii) Change in momentum, Δp = {Ft =} EqL / v

(iii)

EITHER

The charged particle is not an isolated system, so the law does not apply

The system is {consists of} the particle and the ‘plates’. There is an equal and opposite Δp {change in momentum} on the plates, so the law applies.