You are about to erase your work on this activity. Are you sure you want to do this?

Updated Version Available

There is an updated version of this activity. If you update to the most recent version of this activity, then your current progress on this activity will be erased. Regardless, your record of completion will remain. How would you like to proceed?

Mathematical Expression Editor

Electic Charges

Electric charges observed in nature are multiples of a charge of an electron C. JJ
Thomson discovered the electron in his cathode ray tube experiments in 1897. R.
Millikan measured the mass to charge ratio of the electron in 1909 through his
oil-drop experiment. In 1960, J. G. King proved experimentally that one proton
carries a positive charge of C.

Electrostatic Force

The electrostatic force acts between electric charges in the following way:

two positive charges repel each other.

two negative charges repel each other.

a positive and a negative charge attract each other.

the force between two charges decreases inversely proportional to the
square of the distance.

the force acts along the line that connects the charges.

in nature, positive and negative charges are balanced, and the net result
is electrical neutrality! Balance is formed by tight fine mixtures of positive
and negative charges.

A demonstration of the electric force by the MIT professor emeritus Walter
Lewin.

_

Coulomb’s Law

What we described is exactly the electrostatic force. All matter is a mixture of
positive protons and negative electrons in a perfect balance. Coulomb described the
strength and direction of the electrostatic force through his torsion-balance
experiment in 1785. We can represent this electrostatic force visually. Figure twostaticch shows a
stationary charge , repelling charge with a force . The figure shows the unit vector ,
and the distance vector , where is the distance between the two point charges. The
equation that describes the electrostatic (Coulomb) force is given in Equation
EqCoulombslaw.

In the above equation, F/m is the electrical permittivity of air, is the distance
between charges, vector is a unit vector oriented from charge 1 to charge 2. The unit
vector is on the line that connects charges 1 and 2, and therefore the electrostatic
force is also on the line that connects the two charges. The force will either point in
the direction of the unit vector if the force is repulsive (charges have the same sign),
or in the opposite direction when the force is attractive (charges have the
opposite sign). Note that we need at least two charges to find the electrostatic
force.

Figure 1: Vector representation of Coulomb’s force between two static charges.

If the total net charge of an object is , and if that object has electrons and protons,
then the total charge is .

Two positive unit charges nC and nC are fixed in air in Cartesian coordinate system
at points and , see Figure FigTwoCharges. Find the electric force that a charge at point A
exerts on charge at point B, and the force that charge at point B exerts on
charge at point A. How would your answer change if one charge becomes
negative?

Figure 2: Electric Field due to a unit charge in Rectangular coordinate system.

The electrostatic force on charge is given by

To find the force, we have to calculate

(a)

The magnitude of the force . To find the magnitude, we need to find the
distance between the two charges . To find the distance, we need to find
the distance vector .

(b)

To find the unit vector, we need to find the distance vector first. .

The distance vector is a particular type of vector that starts at one point in the
coordinate system and ends at another point. To find the distance vector , we first
have to know the position of charge , where the distance vector starts, and the
position of charge where the distance vector ends. In this problem, the
location of two charges is given by two points in the coordinate system A and
B.

The next step is finding the position vector of point A, and the position vector of
point B. Position vectors are special vectors that start in the coordinate system
origin and point to various points in the coordinate system. Charge is at
point , therefore the position vector of this point is shown in Equation
Eqposvec1.

The position vector of charge is

The two vectors mark the beginning and the end of the distance vector between
charges and . The vector is the sum of vectors and .

When we substitute position vectors and :

The magnitude of vector is

Unit vector in the direction of vector is:

Substituting expressions for , and in equation for the electrostatic force

We get

What if the charge is in an insulator (aka dielectric) other than air?

If the charge is within a dielectric material, then we need to account for that by
changing this somehow. If we place the charge inside a dielectric material, what do
you think will happen with the atoms in the material? The atoms will get
distorted and polarized. Such a polarized atom we call an electric dipole.
The distortion process is called polarization. Because the material polarizes,
the electric field around this point charge is different than if there was no
material. To compensate for this new polarization, we multiply the dielectric
permittivity of free space with a unitless quantity of . is called a relative dielectric
constant. values for different materials can found on the internet. Some
examples of dielectric constants are : air =1, Teflon =2.2, glass =4.4, Silicon
= 11, GaAs =12, distilled water = 80. Equation EqCoulombslaw3 is the definition of the
electrostatic force between two charges. Sometimes, the product of is written as
.

Principle of Superposition

The principle of superposition states that in linear systems, we can calculate
contributions of forces individually from different charges, then add them all up to
get the total force on a charge.

If we have three or more charges, the total force from two charges to one charge is
equal to the vector sum of the forces due to individual charges, see Figure
UnitCh.

Figure 3: Electric Field due to two charges.

The force on the yellow charge below from charges and are:

Where and are unit vectors in the direction of and . The total field due to both
charges is

Calculate the total force on a positive charge at a point due to two other postive
charges at a point and charge at a point

Figure threecharges shows the charges, distance vectors, position vectors and forces on charge .
The total force is equal to the sum of two individual forces from charges and
.

Where ist the distance vector from charge to and , is the distance vector from
charge to .

Figure 4: Electric field due to two charges in Rectangular coordinate system.

Three positive charges, each are placed at A(0,0), B(8,0), and C(4,4). Calculate the
magnitude and direction of total force exerted on B due to charges A and C. Check
your result with the calculator below. Explore with the calculator below how would
the direction of the net force on B change if the charges A and C become negative.

Four negative charges Q are distributed at (-1,0), (1,0), (0,1) and (0, -1). If we
place the fifth charge Q at the origin (0,0), what will be the total force on
this charge regardless of it’s polarity?

Not enough information

Now, take a look at the simulation of the Baloon experiment. Charge the
baloon by rubbing it on the sweater, then bring it to the wall. What happens?
Observe how the neutral balloon is not attracted to the wall or sweater.
When you rub it on the sweater, it will become attracted to the neutral wall.
Why?

A live demonstration of the electrostatic force between charged and charged,
and charged and neutral body.Charging by induction. Observe the types
of materials: metals and dielectrics (insulators). Towards the end of the
video is a live demonstration of the balloon experiment you worked on in
Geogebra app. The demonstration is by the MIT professor emeritus Walter
Lewin.