Fields and Electrical Physics 1 COULOMB’S LAW Oppositely charged particles experience force of attraction; similarly charged particles experience force

Fields and Electrical Physics

1

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.

+

-

+

r

F F

Q1 Q2

-

Q1 Q2

FF

r

+ -

Q1 Q2

F F

r

Coulomb’s Law

F = force, Newtonsk = constant, 9109Nm2C-2

Qn = charge, Coulombsr = distance, meters

221

r

QkQF


2

ELECTRIC FIELDS (1)

+

+-

+ Isolated negative charge

Force experienced by positive charge

- +

• 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


3

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


4

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


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


6

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


7

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?

+

Same size area A

Flux ψLarge value ofD = ψ/A

Small value of D = ψ/A


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


9

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: 8.8410-12 for a vacuum, 6.610-8 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


10

FIELD INTENSITY AND VOLTAGE

+ -

+ V -volts

E

d• 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?

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Fields and Electrical Physics 1 COULOMB’S LAW Oppositely charged particles experience force of attraction; similarly charged particles experience force