Electric Field Strength

The electric field strength at any point within the field will always be equal, because it is a uniform field.

To calculate the electric field strength between two parallel plates we can use the equation:

E = \dfrac{V}{d}

• E is the electric field strength in volts per metre \left(\text{Vm}^{-1}\right).
• V is the potential difference between the plates in volts \left(\text{V}\right).
• d is the distance between the plates in metres \left(\text{m}\right).

Example: Two parallel plates are connected to a power source providing a d.c supply of 6 \: \text{V}. Calculate the electric field strength when the plates are separated by 0.1 \: \text{m}.

[1 mark]

E = \dfrac{V}{d}

E = \dfrac{6}{0.1}

E = 60 \: \text{Vm}^{-1}

The charged particle will always be attracted to the oppositely charged plate and deflected away from the same charged plate. It will move in a parabola as shown in the diagrams above until it collides with the plate.

To increase the amount of deflection we may:

• Increase the charge.
• Decrease the velocity of the particle.
• Decrease the mass of the particle.

The diagram below shows a proton whose deflection has been increased, as a result of either increased charge, decreased velocity, or decreased mass of the moving charge.

Work done moving a charged particle

If we wanted to know the work done when moving a charge between two parallel plates, we can derive our own equation:

Work done: W = Fd

For a moving charge: F = EQ and d = \dfrac{V}{E}

Substituting F and d into the equation for work done, we arrive at:

W = Q \Delta V

We can see that in the radial electric fields, the field lines get further apart as distance from the particle increases. This represents the changing electric field strength with distance for a radial electric field.

To calculate the electric field strength at any point in the radial electric field, the following equation may be used:

E = \dfrac{Q}{4 \pi \epsilon_0 r^2}

• Q is the charge of the point charge that is causing the field in Coulombs \left(C\right).
• \epsilon_0 is the permittivity of free space, \left(8.85 \times 10^{-12}\right).
• r is the distance from the centre of the charge in metres \left(\text{m}\right).

Example: Calculate the electric field strength at a distance of 0.5 \: \text{mm} away from a proton.

[2 marks]

E = \dfrac{Q}{4 \pi \epsilon_0 r^2}

E = \dfrac{1.6 \times 10^{-19}}{\left(4 \pi \times 8.85 \times 10^{-12} \times \left(0.5 \times 10^{-3}\right)^2\right)}

E = 5.75 \times 10^{-3} \: \text{Vm}^{-1}