Electric Fields

Static Electricity

Many plastic materials can be charged by rubbing them with a cloth. This process involves electrons being transferred from the plastic to the cloth. This makes the plastic have a net positive charge.

Electrons are responsible for materials becoming charged in most situations. Uncharged atoms have an equal number of protons and neutrons, and Ions have an imbalance, therefore a net charge.

Experiment: The Shuttling Ball

The shuttling ball experiment demonstrates that current is a flow of charge. The set-up of the experiment is as the animation shows below: Two plates, one connected to the positive terminal, one connected to the negative terminal:

Animation from Pbworks

Field Lines and Patterns

The field lines of a magnetic field show the path a positive test charge would take if in the field. The diagram below shows the electric field setup between two charged plates. It is often more intuative to picture field lines are going from “positive to negative” then having to consider the path of a test charge:


As with Gravitational fields, an Electric field can be Uniform or Radial.

Uniform fields have constant field strength anywhere in the field. This is characterised by field lines staying the same distance apart anywhere in the field, as the closer the field lines, the stronger the electric field at that point. The field between two parallel charged plates is uniform (see diagram above), however you must be careful with plates, because at the edges of the plates the field lines will bend, and the field is not uniform there:

Radial fields have the characteristic that the further from the charge “source” you travel the weaker the electric field. This means that the field lines in a diagram will diverge, as you get further from the source. The diagram below shows the field lines around a negative point charge. This means that the field lines will be going “into” the point charge (as field lines go from positive to negative).

Electric Field Strength

Electric field strength in an electric field is the force per unit charge a positive test charge is subject to, in that field. Electric field strength is usually denoted by the capital letter E. Thus field strength is given as:

 E=\frac{F}{Q}

Electric Potential Energy

Electric Potential

Electric potential is defined as the work done, per unit positive test charge in moving it from infinity to that point in the electric field. This means that it is the work done to move a charge of 1 C to that point in the test charge from the point of zero potential. This is equivalent to the potential energy, per unit charge. 

 V=\frac{E_{p}}{Q}

In electric fields work is done in moving a positive test charge closer to a positive charge, this is why potentials around a positive charge are positive (work needs to be done). Around a negative charge work needs to be done to move a positive test charge away from the negative charge. Thus “negative work” is done in moving the positive charge towards the negative charge.

Potential Gradients

Coulomb’s Law

Point Charges

Capacitors

What are Capacitors?

Capacitors are electrical components used to store charge, and in doing so, allow a current to smoothly discharge when a break in a circuit occurs. They do this by having two conductive plates, separated by an insulating dielectric. This prevents a current flowing between the two plates, and creates an uniform electric field between the two plates, as long as there is a potential difference across the two plates.

The capacitance (C) of a capacitor is the charge stored across the parallel plate per unit potential difference across the capacitor. A higher capacitance means a greater charge can be stored for a given p.d. The units of capacitance is the Farad (F), though in reality, most capacitors have tiny capacitances in the pico- or nano- range:

  C=\frac{Q}{V}

Energy Stored in a charged Capacitor

When a capacitor is charged energy is stored as electric potential energy. If you plot the potential difference across the capacitor against the charge stored on the capacitor the area under the curve will be equal to the work done by the cell in forcing the electrons (the charge) onto the negative plate, and taking them off the positive plate. Since the work done by the cell in charging the capacitor must be equal to the energy stored by the capacitor (energy must be conserved) the energy stored by the capacitor is the area under such a curve. Since the curve is linear the area under (and hence the energy stored):

 E= \frac{1}{2} QV

Since we also know that  C=\frac{Q}{V}, we can substitute into the energy stored equation to get variations of the function for when we have different unknowns to work out:

 E= \frac{1}{2} QV=\frac{1}{2} CV^{2}=\frac{1}{2}\frac{Q^{2}}{C}

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Capacitor Discharge through a fixed resistor

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