Physics 2102 Gabriela Gonz lez Physics 2102 Introduction to Electricity Magnetism and Optics Charles Augustin de Coulomb 1736 1806 Atomic structure negative electron cloud nucleus of positive protons uncharged neutrons Z atomic number of protons of electrons in a neutral atom A mass number of protons Z of neutrons N electron charge e 1 6 x 10 19 Coulombs proton charge electron mass 9 10938188 10 31 kilograms proton mass 1 67262158 10 27 kilograms neutron mass Charges in solids In a conductor electrons move around freely forming a sea of electrons This is why metals conduct electricity Charges can be induced moved around in conductors Blue background mobile electrons Red circles static positive charge nuclei Insulating solids In an insulator each electron cloud is tightly bound to the protons in a nucleus Wood glass rubber Note that the electrons are not free to move throughout the lattice but the electron cloud can distort locally How to charge an object An object can be given some excess charge giving electrons to it we give it negative charge or taking electrons away we give it positive charge How do we do charge an object Usually moving charges from one surface to another by adhesion helped by friction or by contact with other charged objects If a conductor the whole electron sea redistributes itself If an insulator the electrons stay where they are put Summary Electric charges come with two signs positive and negative Like charges repel opposite charges attract with a magnitude calculated from Coulomb s law F kq1q2 r2 Atoms have a positive nucleus and a negative cloud Electron clouds can combine and flow freely in conductors are stuck to the nucleus in insulators We can charge objects by transferring charge or by induction Electrical charge is conserved and quantized What are we going to learn A road map Electric charge Electric force on other electric charges Electric field and electric potential Moving electric charges current Electronic circuit components batteries resistors capacitors Electric currents Magnetic field Magnetic force on moving charges Time varying magnetic field Electric Field More circuit components inductors All together Maxwell s equations Electromagnetic waves Optical images Matter waves Electric Fields Electric field E at some point in space is defined as the force experienced by an imaginary point charge of 1 C divided by 1 C Note that E is a VECTOR Since E is the force per unit charge it is measured in units of N C We measure the electric field using very small test charges and dividing the measured force by the magnitude of the charge Electric field of a point charge 1 C q E R k q E 2 R Superposition Question How do we figure out the field due to several point charges Answer consider one charge at a time calculate the field a vector produced by each charge and then add all the vectors superposition Useful to look out for SYMMETRY to simplify calculations Example Total electric field 2q q 4 charges are placed at the corners of a square as shown What is the direction of the electric field at the center of the square q y 2q a Field is zero b Along y c Along x x Electric Field Lines Field lines useful way to visualize electric field E Field lines start at a positive charge end at negative charge E at any point in space is tangential to field line Field lines are closer where E is stronger Example a negative point charge note spherical symmetry Electric Field of a Dipole Electric dipole two point charges q and q separated by a distance a Common arrangement in Nature molecules antennae Note axial or cylindrical symmetry Play hockey with electric charges and learn http phet colorado edu en simulation electric hockey Electric Field ON axis of dipole q a q P x Superposition E E E kq E 2 a x 2 1 1 E kq 2 2 a a x x 2 2 E kq 2 a x 2 2xa kq 2 2 2 a x 4 Electric Field ON axis of dipole E kq 2 xa 2 2 2 a x 4 p qa dipole moment VECTOR 2kpx 2 2 2 a x 4 What if x a i e very far away 2kpx 2kp E 4 3 x x E p r 3 E p r3 is actually true for ANY point far from a dipole not just on axis Summary Electric field is the electric force on an imaginary unit positive charge Electric field lines start or end in electric charges When fields are strong electric field lines get closer Electric field of a single charge is E kq r2 The dipole moment vector p has magnitude qa and direction from ve to ve charge Far from a dipole E kp r3
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