Book Reference : Pages 76-78Book Reference : Pages 76-78

1.1. To examine the concept of Electric field To examine the concept of Electric field strength (two ways)strength (two ways)

2.2. To examine the factors which affect the To examine the factors which affect the nature of an electric fieldnature of an electric field

Previously we saw that a field line in an Previously we saw that a field line in an electric field is the path a small positive electric field is the path a small positive charge would take if it were free to move.charge would take if it were free to move.

If this charge is moved by the field then it If this charge is moved by the field then it must be experiencing a forcemust be experiencing a force

The electric field strength, E at a point in an The electric field strength, E at a point in an electric field is defined as the force per unit electric field is defined as the force per unit charge on a positive test charge placed at charge on a positive test charge placed at that pointthat point

E = F / QE = F / Q

Where E is the electric field strength Where E is the electric field strength (N/C(N/C**), F is the Force experienced(N) and Q ), F is the Force experienced(N) and Q is the charge in Coulombs (C)is the charge in Coulombs (C)

Note that E is a Note that E is a vectorvector quantity in the identical quantity in the identical direction to F and is the same as the direction of direction to F and is the same as the direction of the field line for a positive charge (opposite the field line for a positive charge (opposite direction for a negative charge)direction for a negative charge)

* Other units to follow* Other units to follow

Under normal conditions Under normal conditions air is a good insulator. air is a good insulator. However, if the electric However, if the electric field strength is high field strength is high enough then the air enough then the air becomes ionised becomes ionised (electrons ripped from (electrons ripped from the molecules). During a the molecules). During a thunderstorm this thunderstorm this happens suddenly and happens suddenly and lightning strikeslightning strikes

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Consider the force F Consider the force F experienced by a small experienced by a small charge +Q in the charge +Q in the uniform electric field uniform electric field between a pair plates between a pair plates separated by d metres separated by d metres which have a potential which have a potential difference (Voltage V) difference (Voltage V) between them.between them.

Note the field lines are : Parallel to each other, perpendicular to the plates and go from the +ve plate to the –ve plate

By rearranging our field strength equation By rearranging our field strength equation (E=F/Q) we can show that the force on Q is:(E=F/Q) we can show that the force on Q is:

F = QEF = QE

If this charge is moved from one plate to If this charge is moved from one plate to another, a distance of d metres by the force another, a distance of d metres by the force F then work is done (W = f x d)F then work is done (W = f x d)

W = QE x dW = QE x d

Definition :Definition :The potential difference V between two points The potential difference V between two points is the work done per unit charge when a small is the work done per unit charge when a small charge is moved through the potential charge is moved through the potential differencedifference

V = W/QV = W/Q

V = W/Q = QEd/Q = Ed (rearrange)V = W/Q = QEd/Q = Ed (rearrange)

E = V/d E = V/d [Note : alternative units for E: V/m)[Note : alternative units for E: V/m)

Any object with a charge will have an Any object with a charge will have an electric field. As the charge increases, so electric field. As the charge increases, so does the strength of the electric fielddoes the strength of the electric field

The more concentrated the charge the The more concentrated the charge the greater the field strengthgreater the field strength

So far for parallel plates we’ve seen the So far for parallel plates we’ve seen the charge spread charge spread evenlyevenly across parallel across parallel platesplates

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With a V shaped plate With a V shaped plate the field lines are the field lines are concentrated at the tip concentrated at the tip since this is where the since this is where the charge is most charge is most concentratedconcentrated

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For a uniform field For a uniform field between parallel plates between parallel plates the charge is spread the charge is spread evenly over the surfaceevenly over the surface

Experimentally it is Experimentally it is possible to show that possible to show that the electric field the electric field strength is proportional strength is proportional to the charge per unit to the charge per unit area on the surfacearea on the surface

E E Q/A Q/A

Like all proportionalities we can turn this Like all proportionalities we can turn this into an equation by introducing a suitable into an equation by introducing a suitable constant of proportionality....constant of proportionality....

00E = Q/AE = Q/A

00 is called “epsilon nought” & has the is called “epsilon nought” & has the value 8.85 x10value 8.85 x10-12-12 Farads/Metre (F/m) Farads/Metre (F/m)

We’ll cover this later.... (Use of We’ll cover this later.... (Use of 0 0 is required is required for A2 but further knowledge is not)for A2 but further knowledge is not)

A Farad is the unit of capacitance and is 1 A Farad is the unit of capacitance and is 1 Coulomb per Volt Coulomb per Volt

““Epsilon nought” is the permittivity of free Epsilon nought” is the permittivity of free space and is the charge per unit volume on space and is the charge per unit volume on a surface in a vacuum which results in a field a surface in a vacuum which results in a field strength of 1 volt per metre between the strength of 1 volt per metre between the plates plates