6.2.3 Uniform electric field

For parallel plates, the electric field strength (E) is uniform and related to the p.d. (V) across the plates and their separation (d). A positive charge will experience a constant force F is placed between the plates. The force is given by the equation F = EQ. The charge will gain energy as it moves from the positive plate to the negative plate:

W = Fd

VQ = EQd

Q = Ed

E = Q/d

NOTE: This equation ONLY works for parallel plates. It is useful in experiments as you only need a voltmeter and ruler to measure V and r, respectively) in order to determine electric field strength (E). As we already know, the unit for E is N C^-1. However, this equation shows us that we can also use V m^-1.

The capacitance of a parallel plate capacitor depends on the separation (d) between the plates.In a vacuum capacitance is proportional to A and inversely proportional to d:

C ∝ A/d

The constant of proportionality is the permittivity of free space (ε0):

C = ε0A/d

When an insulator other than a vacuum is used between the plates the equation for capacitance uses εr. εr is the permittivity for the insulator. This is always greater than ε0 so εr is sometimes known as relative permittivity:

ε = εr + ε0

This means that the equation for capacitance may be written as:

C = εA/d

Charged particles can be accelerated by electric fields. For example, if in between two oppositely charged horizontal plates, the charged particle will experience a constant electrostatic force because of the uniform electric field between the plates, so it has a constant acceleration. The following ideas can be used to determine the motion of a charged particle between plates:

• Electric field strength 'E'' between the plates = V/d
• force 'F' on the charged particle is given by F = EQ (Q is the charge of the particle)
• work done on the charged particle = Vq (q is the charge of the particle)

An electron travelling in the direction of the electric field from a positive to a negative plate will experience a deceleration. For charged particles moving in an electric field we see that:

• For the horizontal motion
• There is no acceleration hence horizontal velocity (VH) is constant with velocity v
• The time 't' spent in the field is given by the equation t = L/v
• For the vertical motion
• The vertical acceleration 'a' of the particle is given by the equation a = F / m = EQ / m
• The initial vertical velocity u = 0
• The final vertical component of the velocity vv as the particle exits the field is given by the equation vv = u + at = 0 + EQ/m x L/v = EQL/mv

picture credit: Kerboodle Physics OCR A textbook