* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download +q - Purdue Physics
Survey
Document related concepts
History of quantum field theory wikipedia , lookup
Fundamental interaction wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Magnetic monopole wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Electromagnetism wikipedia , lookup
Speed of gravity wikipedia , lookup
Maxwell's equations wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Lorentz force wikipedia , lookup
Circular dichroism wikipedia , lookup
Field (physics) wikipedia , lookup
Transcript
Which graphical representation of electric field of a point charge is correct? A B _ C D _ E) I do not know + + E 1 Q rˆ 2 40 r A E _ 1 Q rˆ 2 40 r What if the magnitude of electric field exactly at the position of a point charge? r 0, E Point charge does not exert field on itself! The Superposition Principle 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 electric field contributed by a charged particle is unaffected by the presence of other charged particles. The Superposition Principle If many more point charges are present (qi) we go for i E i and eventually for integral ! System consists of two point charges (+4) and (+1) +4 +1 How many points exist in space where E-field is equal zero? A) B) C) D) E) None One Two Infinite number I don’t know E-field in the middle of uniformly positively charge ring is represented by y What is about any other point inside the ring? x A) B) C) D) Red arrow Blue arrow Zero I do not know The E of a Uniformly Charged Sphere Can calculate using principle of superposition: 1 Q Esphere rˆ 2 40 r Esphere 0 for r>R (outside) for r<R (inside) The Superposition Principle The electric field of a dipole: Electric dipole: Two equally but oppositely charged point-like objects s -q +q Example of electric dipole: HCl molecule What is the E field far from the dipole (r>s)? Dipoles are ubiquitous 1. Atom will become dipole when it experiences electric field: 2. Some molecules exist in the form of permanent dipoles: HCl molecule In Protein the carbonyl groups of polypeptides have substantial dipole moments and their electrostatic interactions make an important energetic contribution to the stability of an a-helix O C + D=3.7 Debye Calculating Electric Field Choice of the origin y s -q +q x z Choice of origin: use symmetry 1. E along the x-axis E1, x E , x E , x E1, x E1, x 1 q 4 0 r s 2 2 1 q 4 0 r s 2 2 1 qr 2 qrs qs 2 / 4 qr 2 qrs qs 2 / 4 4 0 1 r s 2 r s 2 2 2qrs 4 0 r s 2 2 r s 2 2 2 Approximation: Far from the Dipole E1, x 1 2 srq 2 2 40 s s r r 2 2 2 2 s s if r>>s, then r r r 2 2 2 E1, x 1 2 sq 40 r 3 E1 1 2sq ,0,0 3 40 r 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. 2. E along the y-axis E 1 q rˆ 2 40 r s s r 0, y ,0 ,0,0 , y ,0 2 2 r r s s r 0, y ,0 ,0,0 , y ,0 2 2 s y2 2 2 E E 1 q 40 s y 2 s , y ,0 2 2 2 1 q 40 s y2 2 s y2 2 2 s , y ,0 2 2 s y2 2 2 s y2 2 2 2. E along the y-axis E 1 q 40 s y 2 2 s , y ,0 2 2 s y2 2 2 1 E2 E E 40 s y2 2 2 E 1 q 40 s y 2 2 qs q 33 2 2 2 s y 2 s , y ,0 2 2 s y 2 2 2 1s,0,0 1 qs ,0,0 if r>>s, then E2 3 4 0 r at <0,r,0> 3. E along the z-axis E1 E2 1 qs ,0,0 3 40 r 1 2sq ,0,0 3 40 r at <0,r,0> or <0,0,r> Due to the symmetry E along the z-axis must be the same as E along the y-axis! at <r,0,0> Other Locations The Electric Field Point Charge: E1 1 q1 rˆ 2 40 r Dipole: for r>>s : y +q z 1 2qs E ,0,0 3 4 0 r x - at <r,0,0> 1 qs ,0,0 3 4 0 r at <0,r,0> 1 qs E ,0,0 3 4 0 r at <0,0,r> E s -q + System consists of two point charges (+1) and (-1) +1 -1 How many points exist in space where E-field is equal zero? A) B) C) D) E) None One Two Infinite number I don’t know Dipole in a Uniform Field F qE Forces on +q and –q have the same magnitude but opposite direction Fnet qE qE 0 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. Dipole Moment x: y, z: E1 E2 1 2qs p ,0 ,0,0 ,0 33 40 rr r>>s 1 qs p ,,00,,00 33 40 r The electric field of a dipole is proportional to the Dipole moment: p = qs p qs, direction from –q to +q Dipole moment is a vector pointing from negative to positive charge Electric Field E F /q E E x, y , z , t Electric field has units of Newton per Coulomb: [N/C] A Fundamental Rationale • Convenience: know E at some r location – know the electric force on any charge: F qE • Can describe the electric properties of matter in terms of electric field – independent of how this field was produced. 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 Coulomb’s law is not completely correct – it does not contain time t nor speed of light c. F 1 q1q2 rˆ 2 40 r E 1 q rˆ 2 40 r v<<c !!! Example Problem y E=? 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 xaxis. Calculate the magnitude of the E field at <0,210-8,0> m. sq Since r>>s: 40 r 3 2 10 19 Nm 2 10 m 1.6 10 C 9 E1, x 9 10 3 2 8 C 2 10 m N E1, x 7.2 104 C E1, x 200Å 1 x 2Å Using exact solution: 4 N E1, x 7.1999973 10 C Interaction of a Point Charge and a Dipole Edipole F F F QEdipole Q 1 2qs ,0,0 3 40 d • 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