1Outline and review Review on Coulomb's Law and electric field. Discussion about electric potential (energy). Coulomb’s Law in electrostatics govern the forces between two point charges:2Review: Coulomb’s Law While magnitude of the force is calculated using the formula in page 1. The direction of the electric force is given by: Force is a vector.The direction of the Coulomb force follows1. The line defined by the two point charges.2. Like charges repel, unlike charges attract.3Review: From Coulomb’s Law to electric field The concept of a field, here electric field, is introduced to provide the medium for electric force of one charge to act over a distance and “instantaneously”on another charge. The definition: More often used:F = q · EWhich carries a different meaning: charge in an electric field experiences a force. testqFFFFEEEE =4Review: connection of Coulomb’s Law and electric field at point charge level When e-field of a point charge is concerned: The direction of the Efield is defined by the direction of a positive test charge.5Review: add up electric fields from charges E field from multiple point charges:When the E field is generated by multiple point charges: A vector sum of E1to Em, here m is the number of charges. E field from charges distributed in a volume V:∑==mii1EEEEEEEE∫=VdEEEEEEEE2iiirqk=EEEE2iirdvkd⋅=ρEEEEwithwith6Review: electric field, field line, force and work Electric field line is introduced to illustrate the field: Field lines start from positive charge, end at negative charge. The direction of the force on a positive test charge is tangent to the field line, or follow the direction of the field line.Hence no two field lines cross. The density represents the field strength. Electric field exerts force on a charge and moves it, doing work on the charge. When the e-field is uniform:dUAUBA BWhen a charge q is moved from point A to point B by the E field, the work the electric field does to the charge is:WAB= F d = qE d= UA – UB = –(UB – UA ) = –ΔUi.e., the work the field does equals the negative change of the potential energy of charge q has in the field.qE7Review: electric field, field line, force and work Electric field exerts force on a charge and moves it, doing work on the charge. When the e-field is NOT uniform:dUAUBA BWhen a charge q is moved from point A to point B by the E field where the field is a function of the location r, the work the electric field does to the charge is:The work the field does still equals the negative change of the potential energy of charge q has in the field.qE(rA) E(rB)rArBBABAABUUdW −=⋅=∫rrrrrrrr )(FFFF8Concepts Electric potential energy and electric potential inside an electric field: A charge inside an electric field has electric potential energy, like a mass in a gravitational field has gravitational potential energy. When the charge is a unit positive test charge, the electric potential energy it possesses equals to the electric potential the field has at that point. Electric field is a vector field: fields from multiple charges are added together through vector addition. Electric potential is a scalar: potentials from fields of different charges are added through scalar addition. This is a lot easier than vector addition. Because electric force is conservative, the work it does to a charge inside the electric field only equals the negative change of the electric potential energy of that charge, has nothing to do with the path the charge took.9Electric potential from charges Electric potential from charges: From a point charge:Qqr10Electric potential from charges11Electric potential from charges Electric potential from charges: From multiple point charges:Q1r1Q2Q3r2r3UA12Electric potential from charges Electric potential from charges: From continuous charges:Charge density ρ,Volume V.qr13Examples Electric potential from a dipole:14Examples15Examples Electric potential from a charge disk:16Examples17Potential and potential difference Like in gravitational potential, the absolute electric potential is meaning less unless a reference point is specified.18Electric potential and electric field19example A region of space has an electric potential described by the equationV(x, y, z) = xyz. Find an expression for the electric field vector in the
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