The student is expected to describe and calculate how the magnitude of the electrical force between two objects depends on their charges and the distance between them.
An imbalance of electrons or protons produces a charge on an object. Electrical forces occur only between charged objects.
Electrical forces are either attractive or repulsive. Like charges repel, opposite charges attract each other.
Using Coulomb’s Law, the magnitude of electrical force between objects can be calculated. It is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb’s Law
There are electrical forces between charged objects. These forces are different from the gravitational forces and originate from charged particles. In general, the magnitude of the electrical force depends upon the charges and the distance between the charged objects. The bigger the electrical charges are, the higher the magnitude would be; the farther the distance between the charged objects is, the weaker the force would be. The accurate relationship between these factors can be expressed mathematically by Coulomb’s Law:
where:
F is the electrical force (in Newtons) between two charged objects,
kc is the Coulomb constant (8.99 x 109 Nm2/C2)
q1 and q2 are the quantities of electrical charges of the two different objects, and
d is the distance between two charged objects.
1 Coulomb “C” equals 6.3 x 1018 elementary charges
1 Elementary charge equals 1.6 x 10-19 Coulomb “C”
Note: You may want to review with students how SI units in the equation for Coulomb’s law cancel out leaving N (newton) as the final unit of force. Also review how to multiply exponents by actually adding exponents and how to divide exponents by actually subtracting exponents. Caution students to be sure to convert the distance between charges to meters, if necessary, before making calculations. And lastly, review the use of least significant figures when rounding final answers. Remind students to perform all calculations in the equation on their calculators before rounding the final answer to the appropriate number of significant figures. Sometimes students will see the value of Coulomb’s Constant rounded to 9.0 x 109.
From Coulomb’s Law, it is clear that the electrical force is proportional to the product of the two charges. The higher the whole product becomes, the stronger the force would be. In the denominator, the distance squared indicates that if the distance between the two charged objects becomes longer, the final force would be weaker. This change is nonlinear. It is inversely proportional to the square of the distance between the charged objects.
Charges
Attraction or Repulsion: The direction of the electrical forces is not always attractive. It could be either repulsive or attractive. The direction depends on the intrinsic properties of the charged objects. If the two objects carry different charges, one positive and the other one negative, the direction is attractive. If both charges are the same, the electrical force is repulsive.
Redistribution: The charge cannot be created and it can only be redistributed. Hence, an imbalance of electrons or protons produces a charge on an object. If an object is in the equilibrium state, there is no significant charge existing on a certain side.
Test Charge: A test charge is an ideal particle whose physical properties, except those being tested, are negligible. This ideal particle does not alter the rest of the whole system. The uniform electric field is an electric field that has the same magnitude and direction throughout the system. It is a basic field since all the electrical properties within this field are the same. If a test charge is in a uniform electric field, the test charges behavior will be the same at any point in the field.
Electromagnetic Forces in Our Lives
In our daily lives, electromagnetic forces are responsible for much of the phenomena we experience. For instance, in the fall when you take off your sweater in a dark room, you may see a spark and hear a pop. That phenomenon is due to charged particles. You may feel that there is a force attracting the sweater; that is the electrical force. Sometimes, when you comb your hair in the morning in front of a mirror, you may see your hair fly up. That is also because of electrical force. Since the air is dry, the electrical charges are accumulated during the process when you use the comb on your hair, and the hair carries the same type of charge. The repulsive electrical forces make your hair stand up.