1. Fields and Electrical Physics
COULOMB’S LAW
Oppositely charged particles experience force of attraction; similarly charged particles experience force of repulsion
F – forces
Q1, Q2 – magnitudes of charges
r – distance between charges
Each particle experiences same force as its counterpart, regardless of which has greater charge
Charges will move in directions indicated by arrows (provided there are no disturbances)
Magnitude of force F is directly proportional to the product of charges Q1Q2, and inversely proportional to r2
Example A 40µC positive charge and a 100µC negative are separated by 50mm. Find the force of attraction between the charges.
Coulomb’s Law
F = force, Newtons
k = constant, 9109Nm2C-2
Qn = charge, Coulombs
r = distance, meters
Fields and Electrical Physics

2. Fields and Electrical Physics
ELECTRIC FIELDS (1)
An electric field is represented by the lines that show the direction of the force on a positive charge placed anywhere in the field
Positive charges are drawn toward the isolated negative charge
The lower figures show the electric field lines in the vicinity of an isolated negative charge and an isolated positive charge respectively
Fields and Electrical Physics

3. Fields and Electrical Physics
ELECTRICAL FIELDS (2)
The lines shown on the previous slide are a pictorial way of visualising the reaction of any positive charge to the presence of a fixed negative charge
There are infinite number of lines, but only a few can be shown
The negative charge is responsible for an electric field that are represented by the lines
Electric field lines are used to predict the behaviour of a positive charge placed anywhere in the field
The charge will experience a force in the direction shown by a line at the point where the charge is placed
For a single isolated positive charge, the electric field lines radiate outward, as any positive charge placed in the vicinity of it would be repelled away from it
Fields and Electrical Physics

4. Fields and Electrical Physics
ELECTRIC FIELDS (3)
When two or more charges occupy a fixed locations in space, electric field pattern depends on the magnitudes of the charges and their locations with respect to each other
Left figure shows electric field established by fixed positive charge in vicinity of fixed negative charge
Lines always originate at a positive charge and terminate at a negative charge: from +ve to –ve
The lines show the direction a positive charge would move if placed in the field
Point charges are fixed points of charges
Right figure shows electric field that results when two sheet charges (charges distributed over surfaces) are placed in the vicinity of each other
Fields and Electrical Physics

5. ELECTRICAL FLUX DENSITY
An electric field pattern shows the direction of force on a positive charge placed in field
It can also be used to show the relative magnitude of the force experienced by a +ve charge placed at any point in the field
Where the lines are close together (dense), force on +ve charge is greater than it is in a region where lines are less dense (see previous slide)
Lines are more closely spaced nearer the charge
Confirmed by Coulomb’s Law: The closer we move a +ve charge to fixed –ve charge, the greater the force on it
Further away from fixed negative charge, field lines are less dense, thus smaller force
Number of lines on field diagram is arbitrary – there are an infinite number of lines for +ve charges to move along
For computational analysis, it is convenient to assume that the number of lines produced by a charge is the same as the charge in Coulombs
Instead of lines, the term electric flux is used, ψ, and has Coulombs as units
Fields and Electrical Physics

6. Fields and Electrical Physics
FLUX DENSITY
The notion of flux, and its units, serves only as a convenient basis for mathematical computations
We could not draw a field diagram showing one one-millionth of a line corresponding to 1µC of flux!
Electrical flux gives us a basis for defining a numerical quantity that reflects how closely spaced the lines are in an electric field
We must visualise the lines in 3D space around a charge
Flux density D is defined to be flux per unit area
D = ψ/A Coulombs/meters2 (Cm-2)
For the above formula to be valid, the surface area used in the computation has to be perpendicular to the flux lines at every point where the flux penetrates the area
Depending on the field pattern, the area A may be a curved surface
Fields and Electrical Physics

7. Fields and Electrical Physics
FLUX DENSITY EXAMPLE
Example One of the areas between two charged surfaces measures 6mm by 8mm, and the flux penetrating it is 96µC. Each of the charged surfaces measures 2.5cm by 4cm. What is the flux density in the region between the charged surfaces? What is the total flux in the region between the charged surfaces?
Suppose that each dimension of the two charged surfaces is doubled, but the total charge on each surface remains the same. What, then, is the flux density in the region between the surfaces?
Fields and Electrical Physics

8. ELECTRIC FIELD INTENSITY
Electric field intensity, also called electric field strength, is the ratio of the force experienced by the charge placed in the field to the magnitude of the charge itself: E = F/Q Newtons/Coulomb (NC-1)
The stronger the field, the greater the force a given charge will experience when placed in the field
Values for E will be different at different points of the field
The field intensity in a region close to a positive charge is greater than it is at a long distance from the charge (see previous slide)
Where the flux is denser in the region near to a fixed charge, the force experienced is greater
Fields and Electrical Physics

9. Fields and Electrical Physics
PERMITTIVITY
Points on previous slide suggest there is a relationship between D and E
Each is related to the magnitude of the force experienced by a charge placed in an electric field
The denser the flux (greater D), the greater the force on such a charge
The greater the field intensity E, the greater the force on the charge
D and E are proportional to each other: D = E
 is a constant whose value depends on the material in which the field is established (air, glass, water, etc.). It is called the permittivity of the material
Typical values are: 8.8410-12 for a vacuum, 6.610-8 for certain ceramics
Example When a 1000µC charge is placed in a certain electric field, it experiences a force of 28.2N. If the field exists in a vacuum, find the field intensity at the point where the charge is placed. Also find the flux density at the point where the charge is placed
Fields and Electrical Physics

10. FIELD INTENSITY AND VOLTAGE
A voltage always exists between two oppositely charged regions
A field is said to be uniform when the flux density of the electric field in a region between two charged surfaces is the same everywhere (assuming two perfectly parallel surfaces as above)
The electric field intensity between two charged, parallel surfaces can be computed from the voltage difference v across the surfaces
The units of E (N/C) are equivalent to V/m
For two charged parallel surfaces: E = V/d Vm-1
Example Two parallel surfaces are separated by 12mm. A 600µC charge placed between them experiences a force of 7.2N. What is the voltage difference between the surfaces?
Fields and Electrical Physics