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Electric fields and potential

At the Museum of Science in Boston! Why isn’t this man electrocuted?


Conceptual Physics, Paul Hewitt, Chapter 33 Electric Fields and Potential

Conceptual Physics textbook

33.1 Electric fields

POWERPOINT Chap 33 Electric Fields and Potential


Earth’s has an invisible gravitational field. This field allows the Earth to interact with something, without actually touching it.

Just like masses have gravitational fields, charged particles have electric fields.

We’ll be mentioning gravitational fields – and later on, electromagnetic field. What exactly is a “field” anyways? See here: What are fields?

33.2 Electric field lines

There are 2 types of electric charges

What is an electric field? It’s like an invisible force field around an object.

Look at the big + charge below.

It is surrounded by a field that we can’t see.

So how do we know that this field exists?

Nail this charge down, so it can’t move.

Then place a + charge near it – and let go. See what happens.

It gets pushed! (Draw the push with a blue arrow)

These blue lines make the invisible field, visible!

Electric field test charge

Here is a + charge, nailed down on the left, and a – charge, nailed down on the right.

Drop a + “test charge” near the left one. Let go. What happens?

Now trace the path of that test charge many times, in different places.

When you trace the results, we see the invisible field!

When you have traced the paths of that test charge many times in many different places, you start to get an idea of what the field map looks like. The completed field map is shown below.

These lines are arrows: the direction shows the motion of the + test charge

Field lines never cross each other

The closer field lines are, the greater the field’s strength.

Another example:

Electric fields app: Electric Field Lines Interactive: PhysicsClassroom.Com

PhET electric fields app: PhET charges and fields

field lines

Electric fields in parallel plates

“Fig. 22.21 Electric field between two oppositely charged parallel plates. The field between the plates is uniform except near the edges, which are ignored.”

Vectors always drawn from + charges to – charges


Electric Field Hockey Virtual Lab

Play hockey with electric charges. Place charges on the ice, try to get the puck in the goal. View the electric field. Trace the puck’s motion.

Learning Goals
Determine the variables that affect how charged bodies interact.
Predict how charged bodies will interact.
Describe the strength and direction of the electric field around a charged body.


33.3 Electric shielding

PhysicsClassroom.Com : Electric fields and conductors

The electric field inside a conductor is zero

If it were not then the electric charges would move

The net charge on a conductor resides on it’s outer surface

Conductors field line

The E-field here is zero. But that’s not a law of nature – just a special case:
We’re only looking at electrostatics: the charges are allowed to spread out (which happens super quickly) and then they stand still.
Yet it is possible to have an electric field inside a conductor: You can put one there by e.g. using a battery. This prompts charges to move inside the conductor – and therefore a current develops.
But this is no longer electrostatics – now it is electrodynamics.
(That requires more complex math to analyze)

How to shield an electric field

A Faraday cage blocks the effects of an electric field.
It can block the effects of an external field on its internal contents, or the effects of an internal field on the outside environment.

A Faraday cage is a closed chamber made of a conducting material, or a mesh of such a material.
Invented by Michael Faraday in 1836, and can block external static and non-static electric fields.
When an external electric field operates on a Faraday cage:
-> charges in the cage rearrange, to directly counteract the field
-> and thus “shield” the interior of the cage from the external field.

faraday cage

“As the field is applied, the negative charge from the cage migrates toward the positive end of the field, canceling the effects of the field at both ends of the cage.”

The action of a Faraday cage may depend on whether or not it is grounded. Consider a charge placed within a cage. If the cage is not grounded, electrons in the cage will redistribute such that the interior wall of the cage takes on a charge opposite the internal charge. This would leave an exterior wall of opposite charge to that of the interior.

If it is grounded, however, excess charges on the exterior of the cage will go to the ground, leaving the exterior wall of neutral charge.

Faraday cages are limited in their effectiveness, and cannot block static and slowly varying magnetic fields, such as that of the planet Earth. They can, however, shield the interior from external magnetic radiation provided that the mesh is smaller than the wavelength of the radiation and that the shield is sufficiently thick.

Applications: Microwave ovens contain energy within themselves, shielding the outside from harmful radiation.

Electrical linemen often wear suits made of Faraday cages so as to avoid electrocution.

Elevators can act as unintended Faraday cages, shielding cell phones and radios from signal from the outside.

Source: Boundless. “Electrostatic Shielding.” Boundless Physics. Boundless, 21 Jul. 2015. Retrieved 29 Jan. 2016 from Electrostatic shielding: Boundless.Com

33.4 Electrical potential energy

Work is done to life the mass against the gravitational field of the Earth.

Once lifted the object has PE (grav potential energy.)

When released PE is lost, but KE (kinetic energy) is gained.

An analogous transfer of energy – from one form to another – occurs for electric charges.


This section is from http://regentsprep.org/Regents/physics/phys03/apotdif/

Here, the work done by the person is 30J

This is also the electrical PE in the three charges altogether.

The electrical potential (not energy) is the amount of energy / charge.

At the original position of the charges, they have no PE, 0 volts.

Once pulled apart, they have have electrical PE of 10 volts.

Electrical potential = amount of energy / unit of charge.

So when one of the charges is released, the E-field does 10 Joules of work on it

So the particle will have KE = 10 Joules, the instant before it strikes the negative charge.


Here the monkey does work on a + particle, bringing it near a fixed (“nailed down”) + particle.

monkey love elec potential energy


33.5 Electric Potential

The following is adapted from Physics: Principles and Problems (Glencoe Science) Section 21.2.  http://www.cttech.org/GOODWIN/academics/science-textbook/chap21.pdf

Consider the change in PE (gravitational potential energy) of a ball when it is lifted.

21-5 Work needed to move an object

Glencoe Science Physics, Chap. 21

Both the weight (gravitational force, F)
and the gravitational field, g = F/m,
point toward Earth.

If you lift a ball against gravity, you do work on the ball, increasing its PE.

Consider 2 unlike charges: they attract each other.
We must do work, to pull one away from the other.

This transfers energy to the moved charge: it’s stored as electrical potential energy.

The larger the charge, the greater the increase in its potential energy, PE.

E = F/q    The electric field is the force per unit charge.

The electric potential difference is symbolized as V

V = Work done moving a + charge between two points in an electric field
        divided by the magnitude of the test charge.

Electric potential difference equation

measured in joules / coulomb


  • View the next figure:
    The negative charge (blue sphere) creates an E-field (pointing toward itself.)

  • place a small + test charge, at position A.

  • It feels a force, in the direction of the E-field.

  • Now move the + charge, to position B.

  • You have to exert a force ( F ) on it!

  • Because F is in the same direction as the displacement,
    the work done on it is positive.

  • Thus there’s a + change in the electric potential difference.

  • ΔV  (change in potential difference) doesn’t depend
    on the magnitude of the test charge.

  • ΔV only depends on the E-field, and displacement

21-6 Electric Potential Difference is determined.JPG

Glencoe Physics Chapter 21


  • Now move the + charge back to A   (right side of figure)

  • That’s opposite the original, so we’re doing negative work.

  • So the ΔV (electric potential difference) is also –

  • In fact, it’s equal and opposite to the ΔV for the move from  A to B.

  • fascinating: ΔV does not depend on the path followed

  • ΔV just depends on the two positions.

  • Is there always a ΔV between the two positions? if we move towards or away, sure!

  • Suppose we move the charge in a circle around the – charge.
    Now the force that the E-field exerts on the charge is perpendicular to the direction we moved it:
    So we do no work.  So ΔV = zero.

  • Whenever ΔV between positions is zero,
    those positions are at equipotential.

— end materiel from Glencoe —

Lines of equipotential don’t have to be circles.
Consider the points below: As we move towards or away from them, the ΔV changes.
But as we follow around the squished ellipsoid shapes, the ΔV stays the the same.

Wow, with just a few different charges, the equipotential lines can take on many shapes 🙂

Only differences in potential energy can be measured.

Check out this roller coaster: How much PE does the ball have at position 1?
It’s PE depends on it’s height. But what is height? ….
Is position 1 measured relative to the lowest position (#7) ?

Marble coaster CPO

CPO Physics

No, wait, check out the photo! Perhaps the height should be measured relative to the tabletop (which is lower than position 7)
Oh…wait… perhaps it should be measured relative to the classroom floor?
Or measure relative to the ground outside the school?
And what if the town is on a hill: should height be measured relative to sea level?
There’s no such thing as ‘absolute’ PE.  All PE is measure relative to something convenient to measure.

CPO roller coaster.jpg

The same is true of electric potential; only ΔV  – differences in electric potential – are important.

ΔV (electric potential difference from point A to point B) = Vb – Va

ΔV is measured with a voltmeter.

33.6 Electrical Energy Storage



Capacitors store electrical energy. How?

Capacitors have many uses in electronic and electrical systems. They are so ubiquitous that it is rare that an electrical product does not include at least one for some purpose.  https://en.wikipedia.org/wiki/Applications_of_capacitors


The battery has chemical reactions which create an electric field

This field pulls charges from one side of the capacitor, pushes them through the battery

Capacitor GIF 1

Now the charges are pushed onto the opposing plate.

top side is missing – charge, and so becomes +
bottom side gains – charge, and so becomes –

Capacitor GIF 2

Result? There is an electric field within it
Stored energy is analogous to gravitational PE

Electric Potential Energy (Joules)


Batteries: Specify the potential difference of the charges within the battery.

D-cell = 1.5 volts

Means that for every Coulomb of charge that moves from the – side to the + side, the battery does 1.5 Joules of work.

AA-cell = 1.5 volts

Only difference between D-cell and AA-cell is that D-cell has more chemicals, so it can do more chemical reactions (“has more energy”), so it was last longer.

D-cell has more energy and can do more work, but works at the same rate (or has the same power) as AA

Every charge that passes through light bulb does 1.5 joules worth of work

This makes bulb heat up & give off light.


3.7 Van de Graaff generator

The Van de Graaff generator was developed in 1929 as a particle accelerator in physics research: it accelerates subatomic particles to high speeds. Today it is still used to generate energetic particle and x-ray beams in fields such as nuclear medicine. Robert J. Van de Graaff  (1901 – 1967) was an American physicist, who taught at Princeton University and Massachusetts Institute of Technology.

Robert J. Van de Graaff

Photo: MIT Museum and Smithsonian Institution, courtesy AIP Emilio Segrè Visual Archives

How do they work?

Images here from PhysicsClassroom.com


See Current Electricity – Lesson 1 – Electric Potential Difference : PhysicsClassroom.com

Si Unit for electric potential : volt

Alessandro Volta Presenting His Great Invention to Napoleon Bonaparte Nov 1800

Alessandro Volta Presenting His Great Invention to Napoleon Bonaparte Nov 1800

Google Doodle in honor of Alessandro Volta’s 270th Birthday


SI (metric) units for the volt

volt = difference in electric potential between 2 points of a conducting wire, when a current of 1 A dissipates 1 W of power between those points.

volt = potential difference between 2 parallel, infinite planes spaced 1 meter apart, that creates an electric field of 1 N/C

volt = potential difference between 2 points, that gives 1 J of energy per C of charge that passes through it.

Can be expressed in terms of SI base units (m, kg, s, and A) as:

A volt can also be expressed as:

amperes times ohms (current times resistance, Ohm’s law)

watts per ampere (power per unit current, Joule’s law)

joules per coulomb (energy per unit charge)

electron volts per elementary charge

– Wikipedia


Clarification: Electrical Energy and Electrical Potential

Two completely different things that sound alike!

In order to bring two like charges near each other – work must be done.

In order to separate two opposite charges, work must be done.

As the monkey does work on the + charge, he increases the energy of that charge.

The closer he brings it, the more electrical potential energy it has.

monkey love elec potential energy

When the monkey releases the charge, work gets done on the charge

this changes its energy from electrical PE to KE

Every time he brings the charge back, he does work on the charge.

If he brought the charge closer to the other object, it would have more electrical potential energy.

If he brought many charges, he’d have had to do more work so he would have created more electrical PE

Electrical potential energy can be measured in Joules just like any other form of energy.

It is helpful to describe the electrical potential energy, per unit of charge.

This is known as electrical potential (NOTE: not same as electrical potential energy)

As a formula:  V = W / q

Energy per unit of charge =  voltage

Work or energy can be measured in Joules. Charge is measured in Coulombs.

So the electrical potential can be measured in Joules per Coulomb which has been defined as a volt.

The above text and images have been adapted from Regentsprep.org

PhET capacitor lab:

Explore how a capacitor works! Change the size of the plates and add a dielectric to see how it affects capacitance. Change the voltage and see charges built up on the plates. Shows the electric field in the capacitor. Measure voltage and electric field.

Sample Learning Goals

  • Determine the relationship between charge and voltage for a capacitor.
  • Determine the energy stored in a capacitor or a set of capacitors in a circuit.
  • Explore the effect of space and dielectric materials inserted between the conductors of the capacitor in a circuit.
  • Determine the equivalent capacitance of a set of capacitors in series and in parallel in a circuit.

Capacitor Lab app: PhET, University of Colorado

Adapted from https://en.wikipedia.org/wiki/Van_de_Graaff_generator

World’s Largest Van de Graaff Generator at the Boston Museum of Science.


Learning Standards

Massachusetts 2016 Science and Technology/Engineering (STE) Standards

HS-PS2-4. Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and predict the effects of gravitational and electrostatic forces between objects.
HS-PS3-1. Use algebraic expressions and the principle of energy conservation to calculate the change in energy of one component of a system… Identify any transformations from one form of energy to another, including thermal, kinetic, gravitational, magnetic, or electrical energy. {voltage drops shown as an analogy to water pressure drops.}
HS-PS3-2. Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields [e.g. electric fields.]
HS-PS3-3. Design and evaluate a device that works within given constraints to convert one form of energy into another form of energy.{e.g. chemical energy in battery used to create KE of electrons flowing in a circuit, used to create light and heat from a bulb, or charging a capacitor.}
HS-PS3-5. Develop and use a model of magnetic or electric fields to illustrate the forces and changes in energy between two magnetically or electrically charged objects changing relative position in a magnetic or electric field, respectively.

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