Quick questions on Electric fields, point charges and parallel plates (QCE Physics Unit 3)

The electric field $\vec{E}$ at a point is the force per unit positive test charge placed there:

Two parallel conducting plates separated by distance $d$ with a potential difference $V$ between them set up a uniform field in the region between the plates (away from the edges):

A charged particle entering a parallel-plate region with a horizontal velocity $v_0$ perpendicular to the field experiences a force only in the field direction. The motion is exactly analogous to a horizontally launched projectile in gravity:

QCAA frequently asks for field-line sketches. Conventions:

Expect a parallel-plate problem with a charged particle accelerated or deflected, asked for the final speed or deflection. Alternatively, a two-charge geometry with a question on the net field at a point. Markers focus on candidates who forget the direction of $\vec{E}$, treat the field of a negative charge as positive, or confuse the field direction with the force direction on a negative test charge.

A field-only IA2 is rare in QCE Physics (typically Topic 2 IA2s use induction or transformers), but design discussions sometimes reference a Millikan-style charged-droplet apparatus or a parallel-plate beam-deflection demo. The theory section then uses $E = V/d$ and $qV = \tfrac{1}{2} m v^2$ to predict speeds and deflections.

State the relationship between the electric field and the potential difference between parallel plates. [2 marks]

Two point charges $+2.0 \text{ nC}$ and $-4.0 \text{ nC}$ are $0.10 \text{ m}$ apart. Calculate the force between them. ($k = 8.99 \times 10^9$).

An electron enters a parallel-plate gap horizontally at $2.0 \times 10^7 \text{ m s}^{-1}$ with plate length $0.08 \text{ m}$ and gap $V = 200 \text{ V}, d = 0.02 \text{ m}$. (a) Calculate the field strength and the vertical acceleration. (b) Determine the transit time and vertical deflection.