Electric charge explains why objects can attract, repel, spark, and interact without touching. This cheat sheet helps students connect charge behavior to Coulomb's law, the main equation for electric force. It is useful for solving force problems, choosing signs and directions, and understanding how multiple charges affect one another.
Students in grades 9-12 need these ideas before studying electric fields, circuits, and electromagnetism.
The most important ideas are that charge is conserved, charge is quantized, and like charges repel while opposite charges attract. Coulomb's law gives the size of the force between two point charges using . The direction of the force depends on whether the charges have the same sign or opposite signs.
When more than two charges are present, the net force is found by adding individual forces as vectors.
Key Facts
- Like charges repel and opposite charges attract, so two positive charges or two negative charges push apart, while a positive and a negative charge pull together.
- Electric charge is conserved, meaning the total charge of an isolated system stays constant: .
- Charge is quantized in multiples of the elementary charge: , where and is an integer.
- Coulomb's law for the magnitude of electric force is , where .
- The electric force gets weaker with distance according to an inverse-square relationship, so doubling makes the force as large.
- The force on charge due to charge has the same magnitude as the force on due to , but the forces point in opposite directions.
- For multiple charges, use superposition: .
- A neutral object has equal amounts of positive and negative charge, so its net charge is .
Vocabulary
- Electric charge
- A property of matter that causes electric forces and can be positive, negative, or zero.
- Coulomb
- The SI unit of electric charge, written as .
- Elementary charge
- The smallest basic unit of free charge, with magnitude .
- Coulomb's law
- The rule that gives the electric force between two point charges: .
- Conductor
- A material in which electric charges can move easily, such as copper or aluminum.
- Insulator
- A material in which electric charges do not move easily, such as rubber, glass, or plastic.
Common Mistakes to Avoid
- Using the wrong distance in Coulomb's law is wrong because must be the center-to-center distance between the charges, not the diameter or surface gap unless the problem defines it that way.
- Forgetting to square the distance is wrong because Coulomb's law uses , so the force changes by the square of the distance change.
- Putting charge signs into the magnitude formula without thinking about direction can lead to confusion because gives magnitude, while attraction or repulsion gives direction.
- Treating charge as something created during rubbing is wrong because charge is transferred, not created, so total charge is conserved.
- Adding forces as ordinary numbers in two-dimensional problems is wrong because electric forces are vectors and must be added using direction, components, or a diagram.
Practice Questions
- 1 Two charges and are separated by . Find the magnitude of the electric force between them using .
- 2 A charge of is placed from a charge of . Calculate the force magnitude and state whether the force is attractive or repulsive.
- 3 An object gains extra electrons. Find its net charge using and the electron charge .
- 4 Two identical metal spheres touch and then separate. One started with charge and the other with charge . Explain conceptually why charge is shared and why the total charge after separation must equal the total charge before contact.
Understanding Electric Charge & Coulomb's Law
At the atomic scale, electric charging usually means electrons have moved from one material to another. Protons are held in atomic nuclei and do not travel through ordinary solids. An object with extra electrons has a negative net charge.
An object missing electrons has a positive net charge. Rubbing a balloon on hair can transfer electrons because the two materials hold electrons with different strengths. The hair and balloon receive equal amounts of opposite net charge.
In dry air, that charge can remain for a while. Humid air provides a thin path for charge to leak away, which is why static effects are often weaker on humid days.
Conductors have electrons that can move through the material. Metals are common conductors because some of their outer electrons are not tightly tied to one atom. Insulators hold electrons much more firmly in place.
Plastic, rubber, glass, and dry air are useful insulators. A neutral conductor can still be attracted to a charged object. Its mobile charges shift slightly inside it.
This rearrangement is called polarization. The closer side develops an excess of the opposite kind of charge, so the nearby attraction can be stronger than the farther repulsion.
Grounding gives electrons a route between an object and Earth. Earth is so large that it can accept or supply many electrons without gaining a noticeable net charge.
Coulomb's law works best when charges can be treated as point charges. This is reasonable when the objects are much smaller than the distance between them. For large objects or objects with charge spread unevenly across their surfaces, the calculation becomes more complicated.
The force depends strongly on separation because the effect of a charge spreads through three dimensional space. If the separation becomes three times larger, the force becomes one ninth as large. Use meters for distance, coulombs for charge, and newtons for force.
A result in newtons describes the push or pull on one chosen charge. The partner charge experiences a force with equal size in the opposite direction. These forces act on different objects, so they do not cancel on either one object.
Problems with several charges need careful organization. Draw the positions first and choose the charge whose net force you need. Find each force on that charge separately.
Mark every force arrow before doing arithmetic. Forces in one straight line can be assigned positive or negative directions. For a two dimensional arrangement, split each force into horizontal and vertical parts, add the horizontal parts, then add the vertical parts.
A zero net force does not mean that no forces are present. It can mean strong forces balance exactly.
Common mistakes include using a signed charge product for force size, forgetting that distance is squared, and adding force sizes without checking direction. A clean diagram prevents most of these errors.