Physics and Math 5 Electrostatics and Magnetism

Physics and Math 5: Electrostatics and Magnetism Essential Equations for Test Day Charges 𝐹: = Coulomb: The SI unit of charge Protons & Protons have a positive charge and electrons have a negative Electrons: charge. Both protons and electrons possess the fundamental unit of charge (𝑒 =1.60'×'10)*+ 'C). Protons and electrons have different masses. Attraction & Opposite charges exert attractive forces, and like charges Repulsion: exert repulsive forces Conductors: Allow the free and uniform passage of electrons when charged Insulators: Resist the movement of charge and will have localized areas of charge that do not distribute over the surface of the material /'|12 |'|13 | 43 𝐸 =' /'I 43 𝑈 =' /'I'1 𝑉 =' 4 /'I 4 Electrical Potential Energy Electrical potential energy is the amount of work required to bring the test charge from infinitely far away to a given position in the vicinity of a source charge. Increases: Like charges move toward each other. Opp charges move apart Decreases: Opp charges move toward each other. Like charges move apart Electrical Potential Energy: 𝑈 ='/'I'1 4 Coulomb’s Law Electrical Potential Coulomb’s Law: Gives the magnitude of the electrostatic force vector between two charges. The force vector points along the line connecting the centers of the two charges. /'|1 |'|1 | 𝐹 = 2 33 4 Electric Field: Every charge generates an electric field, which can exert forces on other charges 1 Field Lines: Used to represent the electric field vectors for a charge. They show the activity of a positive test charge, which would move away from a positive charge and move toward a negative charge (north to south). The field is stronger where the field lines are closer together. Special Cases in Electrostatics Equipotential A line on which the potential at every point is the same. Lines: Equipotential lines are always perpendicular to electrical field lines. Work will be done when a charge is moved from one equipotential line to another. No work is done when a charge moves from a point on an equipotential line to another point on the same line. Electric Dipole: Generated by two charges of opposite sign separated by a fixed distance d. In an external electric field, an electric dipole will experience a net torque until it is aligned with the electric field vector. An electric field will not induce any translational motion in the dipole regardless of its orientation with respect to the electric field vector. /'1'Y 𝑉 =' 3 'cos'( q ) 4 Net Torque: t '=𝑝'𝐸'sin'( q) Dipole The product of charge and separation distance Moment: 𝑝=𝑞'𝑑 Electrical potential is the electrical potential energy per unit charge. Different points in the space of an electric field surrounding a source charge will have different electrical potential values. Electrical Potential: From electrical potential energy L Q 𝑉 =' 1'volt=1' 1 Voltage: R Potential difference. The change in electrical potential that accompanies the mvmt of a test charge from one position to another. V ∆𝑉=𝑉 T −𝑉 ? =' WX1 Test Charges: Will move spontaneously in whichever direction results in a decrease in their electrical potential energy. POS Test Charges: High potential Low potential NEG Test Charges: Low potential High potential Magnetism Magnetic Field: Created by magnets and moving charges. SI unit is the tesla (T). 1'T=10,000'gauss µ 'i Loop of Wire: 𝐵 =' Straight Wire: 𝐵 =' j' hp '4 µ h 'i j'4 Diamagnetic Possess NO unpaired electrons and are slightly REPELLED Materials: by a magnet Paramagnetic Materials: Ferromagnetic Materials: Characteristics of Magnetic Fields: Possess SOME unpaired electrons and become WEAKLY MAGNETIC in an external magnetic field Possess SOME unpaired electrons and become STRONGLY MAGNETIC in an external magnetic field Current-carrying wires create magnetic fields that are concentric circles surrounding the wire. External magnetic fields exert forces on charges moving in any direction except parallel or antiparallel to the field. Point charges may undergo uniform circular motion in a uniform magnetic field wherein the centripetal force is the magnetic force acting on the point charge. Determine direction using the right-hand rule. Moving Point Charge: 𝐹k =𝑞'𝑣'𝐵'sin'(q) Current-Carrying Wire: 𝐹k =𝐼'𝐿'𝐵'sin'( q ) Lorentz Force: Sum of the electrostatic and magnetic forces acting on a body