* The Physical Concept of ‘Field’ Field: physical quantity, can be scalar or vector Examples: Temperature T(x,y,z,t) Gravitational field m q * How Strong is the Coulomb Force eletron and proton * A penny carrying a small amount of positive charge Qp exerts an electric force F on a nickel carrying a large amount of positive charge Qn that is a distance d away (Qn > Qp ). Which one of the following is not true? The electric force exerted on the penny by the nickel is also equal to F. B. The number of electrons in the penny is less than the number of protons in the penny. C. , if d is small compared to the size of the coins. D. , if d is large compared to the size of the coins. Question 1 (Chap. 13) * Which one of the following is not true? The electric force exerted by an electron on an electron: A. decreases by a factor of 25 if the distance is increased by a factor of 5. B. has the same magnitude as the electric force exerted by a proton on a proton at the same distance. C. has the same direction as the electric force exerted by a proton on a proton at the same distance. D. is much weaker than the gravitational force between them. Question 2 (Chap. 13) * The net electric field at a location in space is a vector sum of the individual electric fields contributed by all charged particles located elsewhere. The Superposition Principle The electric field contributed by a charged particle is unaffected by the presence of other charged particles. * The Superposition Principle * The E of a Uniformly Charged Sphere Can calculate using principle of superposition: for r>R (outside) for rs)? +q -q s Example of electric dipole: HCl molecule The Superposition Principle The electric field of a dipole: * Another kind of dipole * +q -q s x y z Choice of origin: use symmetry Calculating Electric Field Choice of the origin * 1. E along the x-axis * if r>>s, then While the electric field of a point charge is proportional to 1/r2, the electric field created by several charges may have a different distance dependence. Approximation: Far from the Dipole at * 2. E along the y-axis * 2. E along the y-axis if r>>s, then at <0,r,0> * 3. E along the z-axis Due to the symmetry E along the z-axis must be the same as E along the y-axis! at <0,r,0> or <0,0,r> at * Other Locations * The Electric Field + - Point Charge: Dipole: for r>>s : at at <0,r,0> +q -q s x y z at <0,0,r> * Example Problem A dipole is located at the origin, and is composed of particles with charges e and –e, separated by a distance 210-10 m along the x-axis. Calculate the magnitude of the E field at <0,210-8,0> m. y 2Å 200Å E=? Since r>>s: Using exact solution: x * Interaction of a Point Charge and a Dipole Direction makes sense? - negative end of dipole is closer, so its net contribution is larger What is the force exerted on the dipole by the point charge? - Newton’s third law: equal but opposite sign * Dipole Moment x: y, z: Dipole moment: p = qs , direction from –q to +q r>>s Dipole moment is a vector pointing from negative to positive charge. The electric field of a dipole is proportional to the * Dipole in a Uniform Field Forces on +q and –q have the same magnitude but opposite direction It would experience a torque about its center of mass. What is the equilibrium position? Electric dipole can be used to measure the direction of electric field. * Demos 5A-10 5A-31 * Choice of System Multiparticle systems: Split into objects to include into system and objects to be considered as external. To use field concept instead of Coulomb’s law we split the Universe into two parts: the charges that are the sources of the field the charge that is affected by that field Example: Oscilloscope Charges on metal plates are the sources of an uniform E field * Convenience: know E at some location – know the electric force on any charge: Example: if E>3106 N/C air becomes conductor Retardation Nothing can move faster than light c c = 300,000 km/s = 30 cm/ns Can describe the electric properties of matter in terms of electric field – independent of how this field was produced. Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. v<>s : at at <0,r,0> +q -q s x y z at <0,0,r> Dipole moment: p = qs Uniformly charged sphere: for r>R (outside) for r