# Work Done in an Electric Field

This is part of the HSC Physics course under the topic Charged Particles, Conductors and Electric and Magnetic Fields.

### HSC Physics Syllabus

• investigate and quantitatively derive and analyse the interaction between charged particles and uniform electric fields, including: (ACSPH083)
work done on the charge W=qV, W=qEd, K=1/2mv^2

### Work Done on Charges in an Uniform Electric Field

This video analyses and quantitatively derives the work done to charged particles as they interact with a uniform electric field.

### Deriving the Work Done

The work done on an arbitrary object is can be calculated by:

W=Fs

Knowing that F=qE, we substitute force F with qE and the displacement with the distance d between a pair of charged plates:

W=(qE)*(d)

W=qEd

Alternatively, can also be expressed in terms electric field strength and potential difference across the metal plates:

d=V/E

thus,

W=qE*(V/E)

W=qV

Note: d is displacement and only equals to the distance between two charged plates if the charged particle is moved from one plate to another. In other words, the second equation only applies when work is done to move a charged particle against the electric field. (diagram below) Work done by electric field can also be analysed by a change in kinetic energy of the charged particle

W=DeltaK = 1/2mv^2-1/2mu^2

where,

•  u and v are initial and final velocities of the charged particle respectively (m s-1)

Practice Question 1

An electron travelling at 50 m/s enters a uniform electric field created by a pair of parallel metal plates connected to a potential difference of 7 V. (a) Calculate the electric field strength. (1 mark)

(b) Calculate the acceleration experienced by the electron upon entering the electric field. (2 marks)

(c) After a short while, the electron is found stationary on the surface of the positive plate. Calculate the work done to move the electron from the positive plate to the negative plate. (1 mark)

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