Understanding Electric Fields

Electric Fields

• The electric field vector (E) has SI units of newtons per coulomb (N/C).
• The direction of E is the direction of the electric force on a positive test charge.
• E exists at a point if a test charge at that point experiences an electric force.
• The electric force on a charge q in an electric field E is given by F = qE.
• If q is positive, F and E are in the same direction; if q is negative, they are in opposite directions.
• To determine the direction of an electric field, a positive test charge is used.
• To calculate the electric field created by a point charge q at a distance r: E = k(q/r^2) r^, where r^ is a unit vector directed from q to the point.
• The total electric field at a point due to a group of source charges is the vector sum of the electric fields of all the charges: E = k Σ (qi/ri^2) ri^ where ri is the distance from qi to the point P and ri^ is a unit vector directed from qi toward P.

Charging Objects by Induction

• Electrical conductors are materials in which some electrons are free electrons, not bound to atoms, and can move relatively freely through the material.
• Electrical insulators are materials in which all electrons are bound to atoms and cannot move freely through the material.
• Semiconductors' electrical properties are somewhere between those of insulators and conductors.
• Electrical properties of semiconductors can be changed over many orders of magnitude by adding controlled amounts of certain atoms.
• To charge a conductor by induction, bring a charged object near it, causing electrons to redistribute.
• The side of the sphere near the rod has an effective positive charge because of the diminished number of electrons.
• A conducting wire connects the sphere to the Earth.
• Since electrons are strongly repelled by the presence of the negative charge in the rod that they move out of the sphere through the wire and into the earth.
• The symbol at the end of the wire indicates that the wire is connected to ground, which means a reservoir.
• If the wire to ground is then removed, the conducting sphere contains an excess of induced positive charge.
• When the rubber rod is removed from the vicinity of the sphere, this induced positive charge remains on the ungrounded sphere.
• Charging an object by induction requires no contact with the object inducing the charge.
• In most neutral molecules, the center of positive charge coincides with the center of negative charge.
• In the presence of a charged object, however, these centers inside each molecule in an insulator may shift slightly, resulting in more positive charge on one side of the molecule than on the other.

Properties of Electric Charges

• When materials behave in this way, they are said to be electrified or to have become electrically charged.
• There are two kinds of electric charges: positive and negative.
• Electrons are identified as having negative charge and protons are positively charged.
• Charges of the same sign repel one another, and charges with opposite signs attract one another.
• Electric charge is always conserved in an isolated system.
• When one object is rubbed against another, charge is not created in the process.
• The electrified state is due to a transfer of charge from one object to the other.
• One object gains some amount of negative charge while the other gains an equal amount of positive charge.
• Negatively charged rubber rod suspended by a string is attracted to a positively charged glass rod
• Negatively charged rubber rod is repelled by negatively charged rubber rod.

Coulomb's Law

• Electric force is sometimes called the electrostatics force.
• From experiments, scientists found that the magnitude of the electric force (sometimes called the Coulomb force) between two point charges is given by Coulomb's law: F = k|(q1q2)|/r^2.
• k is Coulomb's constant, equal to 8.9876 x 109 N⋅m2/C2.
• The SI unit of charge is the coulomb (C).
• Coulomb's constant is also written as k = 1/(4πε0).
• ε0 is the permittivity of free space, equal to 8.8542 x 10-12 C2/N⋅m2.
• The smallest unit of free charge e known in nature has a magnitude of 1.60218 x 10-19 C.
• The electric force is a vector quantity and must be treated accordingly.
• Coulomb's law in vector form: F12 = k (q1q2/r^2) r^12 where r^12 is a unit vector directed from q2 toward q1 as shown in Figure 23.6a
• The force exerted by q1 on q2 is equal in magnitude to the force exerted by q2 on q1 and in the opposite direction.