ELECTROSTATICS
An object becomes electronically charged when the number of protons and electrons do not balance. Static electricity results when this charge is isolated on an object by insulating material.
Excess electrons – object will be charged negatively.
Deficit of electrons – objects will be positively charged.
When one object is rubbed by another electrons are often transferred. If a one or both objects are insulators or insulated then static electricity results.
THE UNIT OF CHARGE
The unit of charge is the COULOMB (C).
1 C = 103mC = 106 µC = 109nC = 1012pC
milli micro nano pico
Convert the following:
456 nC = ………………………………….… C0,78pC = ………………………………. C
2,88 x 10-7 C = ……………………….. µC0,056 C = ……………………………… mC
LAW OF CONSERVATION OF CHARGE
The algebraic sum of the electric charges in a closed system remains constant.
e.g.Two identical metal spheres, one with a charge of -2 nC and the other with a charge of +7 nC, touch one another and are then separated. What will be the charge on each sphere?
(Questions page 96 in book 11)
ELECTROSTATIC FORCES
LIKE CHARGES REPEL UNLIKE CHARGES ATTRACT
COULOMBS LAW
The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between their centers.
F α Q1.Q2F α 1/r2
NOTE!1) Q must be in coulombs and r must be in meters. (Errors with this and forgetting to square r are the most common mistakes made.)
2) Q values are always entered as positive values.
Note:All values for charges must be a multiple of the magnitude of a charge of a single electron (or single proton) (Qe = -1,6 x 10-19 C).
N = Q/Qe
e.g. How many electrons have been removed from an object which has a charge of +4,82nC?
Examples:
1.An object with a +1,8 nC charge is placed 5,2 cm from an object with a charge of -8,0 nC.
a)Calculate the force the +1,8nC object exerts on the -8,0 nC object.
b)How many excess electrons on the -8,0nC object?
2.Two identically charged objects, placed 46 mm apart, exert a force on each other of 1,2 x 10-3 N. What is the charge on each object?
3.Two identical metal spheres, one with a charge of +8 μC and the other with a charge of +25 μC, touch one another and are then separated to a distance of 8,0cm. What force do they exert on each other?
Calculations involving 3 charged particles.
Look at the example of page 97 and then answer the questions below:
- Three charged particles X, Y and Z are set out as shown below.
XYZ
The charge on X is +4 nC and on Y is +3 nC.
a)Calculate the magnitude of the force acting on Y as a result of its interaction with X.
b)In which direction is this force, left or right?
The resultant force on Y as a result of its interaction with X and Z is 1,5 x 10-5 N left.
c)Calculate the magnitude and direction of the force which acts on Y as a result of its interaction with Z.
d)Draw a labelled free-body vector diagram of the electrostatic forces acting on Y.
e)What charge is Z – positive or negative?
f)Calculate the charge on particle Z.
Calculations involving 3 charged particles with a right angle.
Example 1:
Particle P has a charge of +1 µC, particle Q of -5 µC and particle R of -2 µC. They are arranged at the corners of a triangle as illustrated below.
north
P
QR
Calculate the resultant electrostatic force on particle Q.
FR on Q = kQ1Q2/r2 = (9x109 x 5x10-6 x 2x10-6)/0,0822 = 13,38 N west
FP on Q = kQ1Q2/r2 = (9x109 x 1x10-6 x 5x10-6)/0,0452 = 22,22 N north
Force diagrams of forces on Q:
Q
F 22,22 N
θ
Fnet = 25,94 N (Pythagoras)θ = tan-1(13,38/22,22) = 31,05o
Therefore Fnet on particle Q = 25,94 N in a direction 31,05o west of north.
Example 2:
In the system below the position and charge on three identical objects A, B and C is indicated.
2.1Calculate the magnitude of the electrostatic force A exerts on B.
2.2Calculate the magnitude of the electrostatic force C exerts on B.
2.3Draw a free body diagram of the electrostatic forces acting on B.
2.4Draw a triangle vector diagram and then calculate the magnitude of the resultantforce on B and its direction relative to the force A exerts on B.
ELECTRIC FIELDS
An electrically charged object always generates an electric field around it.
Definition: An electric field is a region of space in which an electric charge experiences a force.
The electric field is continuous around an object but we use electric field lines to represent the field.
An electric field line is a line drawn in such a way that a small positively charged object placed on the line will experience a resultant force at a tangent to the line at that point.
Properties of electric field lines:
- They start on positive charges and end on negative charges.
- They never cross.
- They are 3-dimensional.
- The denser the field lines the stronger the field.
- They enter and leave charged object at right angles.
- They are continuous (although drawn as separate lines).
/ Two equally negatively charged objects
(Extension)
Hollowmetal ring
/ (Extension)
Non-spherical object
Parallel plates (extension)
ELECTRIC FIELD STRENGTH
Definition: The electric field strength (E) at a point in an electric field is the force experienced per unit positive charge placed at that point.
Units: N.C-1
e.g. What is the force exerted on an 8,06nC charge in an electric field with a strength of 4000 N.C-1?
Consider a small charge qplaced in the field of a large charge Q at a distance of r.
Force on q:F = E.q and F = (k.Q.q)/r2
Therefore E.q = (k.Q.q)/r2
(q cancels)
e.g.What is the electric field strength at a distance of 24 mm from an object with an excess of 3,5 x 107 electrons? (Qe = -1,6 x 10-19 C)
Note: If a charged object (q) is placed between two other charged objects (Qa and Qb), then each object acts independently producing the field which acts upon it.
e.gCalculate the total force acting upon the charged object X in the system belowby first calculating the resulting electric field at X.