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Key Ideas in Chapter 14: Electric Field A charged particle makes an electric field at every location in space (except its own location). The electric field due to one particle affects other charged particles. The electric force on a charged particle is proportional to the net electric field at the location of that particle. The Superposition Principle: The net electric field at any lecation is the vector sum of the individual electric fields of all charge particles at other locations. The field due to one charged particle is not changed by the presence of other charged particles. An electric dipole consists of two particles with charges equal in magnitude and opposite in sign, separated by a short distance. Changes in electric fields travel at the speed of light ("retardation"). 1 The Coulomb Force Law Key Idea: Charges exert forces on each other Q1 Q2 F F 1 Q1Q2 F= r̂ 2 4pe 0 r Direction of Force is: ATTRACTIVE if charges have OPPOSITE sign REPULSIVE if charges have SAME sign Always acts along a line connecting the charges 2 Which way does the field point? Key Idea: A charged particle makes an electric field at every location in space q1 E1 = r̂ 2 4pe 0 r 1 Point Particle Here is a useful mnemonic: + Positive people care about others -- Negative people care only about 3 themselves iClicker A penny carrying a positive charge Qp exerts an electric force of magnitude F on a nickel carrying positive charge Qn that is a distance d away (Qn > Qp ). Which one of the following is not true? A. 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. The number of electrons in the penny is larger than the number of protons in the penny. 1 Qp Q n D. F ≈ , if d is large compared to the size of the 2 4 pe0 d coins. 4 How Strong is the Coulomb Force? Example: Hydrogen Atom = proton and electron Felec = Fgrav = Felec Fgrav Electricity is much stronger than Gravity 5 Electric Field of Point Charges Key Idea: A charged particle makes an electric field at every location in space (except its own location). 1 Q1Q2 F= r̂ 2 4pe 0 r F2 = q2 E1 What happens as q1 E1 = rˆ 2 4pe 0 r 1 ? Can the particle exert a force on itself? No. E is undefined at the origin, since is self-contradictory. 6 would it point? If there were a force at the origin, which way Electric Field of a Uniformly Charged Spherical Shell q1 E1 = rˆ 2 4pe 0 r 1 for a point particle What should the electric field look like from far away? Esphere Q = rˆ 2 4pe 0 r 1 for r >> R Which direction does the field point close to the sphere? Spherical symmetry The field is in the direction even close up to the sphere 7 Electric Field of a Uniformly Charged Spherical Shell We'll calculate the whole thing in Ch. 16 using the principle of superposition: Esphere Q = rˆ 2 4pe 0 r 1 Esphere = 0 for r >R (outside) for r <R (inside) 8 The Superposition Principle Key Idea: 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. Key Idea: The electric field contributed by a charged particle is unaffected by the presence of other charged particles. 9 The Superposition Principle The electric field of a dipole: Electric dipole: Made of 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)? 10 Calculating Electric Field Choice of the origin y s -q +q x z Choice of origin: use symmetry 11 1. E along the x-axis q1 E1 = rˆ 2 4pe 0 r 1 E1, x = E+, x + E-, x= E1, x = E1, x = Point Particle q 1 4pe 0 ( r - s 2 ) 2 + -q 1 4pe 0 ( r + s 2 ) 2 1 qr + qrs + qs / 4 - qr + qrs - qs / 4 2 4pe 0 1 2 2 2 ( r - s 2) ( r + s 2) 2 2qrs 4pe 0 ( r - s 2 ) ( r + s 2 ) 2 2 2 Dipole Electric Field (Along 12 X-Axis) Far from the Dipole along the x-axis E1, x = 2 srq 1 2 2 4pe 0 æ sö æ sö çr - ÷ çr + ÷ 2ø è 2ø è Dipole Electric Field (Along X-Axis) To find the Electric field far from the dipole (r >> s): 2 2 sö æ sö æ 2 çr - ÷ » çr + ÷ » r 2ø è 2ø è 1 2 sq E1 = ,0,0 3 4pe 0 r Electric Field of Point Particle: ~ 1/r2 Electric Field of Dipole: ~ 1/r3 E1, x 1 2 sq = 4pe 0 r 3 Dipole Electric Field (Far Away Along X-Axis) 13 2. E along the y-axis q1 E1 = rˆ 2 4pe 0 r 1 for a point particle ü s s r+ = 0, y ,0 - ,0,0 = - , y ,0 ï 2 2 ï ý Þ r+ = r- = s s r- = 0, y ,0 - - ,0,0 = , y ,0 ï ïþ 2 2 E+ = æsö y +ç ÷ è2ø 1 q 4pe 0 æsö y2 + ç ÷ è2ø s - , y ,0 2 2 2 æsö y2 + ç ÷ è2ø 2 2 E- = 1 -q 4pe 0 æsö 2 y +ç ÷ è2ø s , y,0 2 2 æsö 2 y + ç14÷ è2ø 2 æsö y2 + ç ÷ è2ø 2 2. E along the y-axis E+ = 1 4pe 0 s - , y ,0 2 q æsö y2 + ç ÷ è2ø 2 æsö y2 + ç ÷ è2ø E- = 2 E2 = E + + E - = æsö y +ç ÷ è2ø 2 1 4pe 0 s - ,- y,0 2 1 q 4pe 0 æsö y2 + ç ÷ è2ø qs q 33 22 22 é 22 æ s ö êy + ç ÷ è2ø êë 2 æsö y2 + ç ÷ è2ø 2 - 1s,0,0 ù ú úû 2 -1 qs ,0, 0 if r>>s, then E2 » 3 4pe 0 r 15 at <0,r,0> 3. E along the z-axis - 1 qs E2 = ,0,0 3 4pe 0 r 1 2 sq E1 = ,0,0 3 4pe 0 r at <r,0,0> at <0,r,0> or <0,0,r> By symmetry, E along the z-axis must be the same as E along the y-axis! 16 Shape of Dipole Electric Field Wikimedia Commons 17 Summary: Point Charge and Dipole Point Charge: q1 E1 = rˆ 2 4pe 0 r 1 Dipole: for r>>s : y s -q +q z x + - 1 2qs E= ,0,0 3 4pe 0 r at <r,0,0> -1 qs E= ,0,0 3 4pe 0 r at <0,r,0> -1 qs E= ,0,0 3 4pe 0 r at <0,0,r> 18 Definition of "Dipole Moment" x: y, z: 1 2qs p E1 = ,0,0,0,0 33 4pe 0 rr r>>s - 1 qs p E2 = ,0,0 3 4pe 0 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 19 charge 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 4 0 r 3 2 10 19 Nm 2 10 m 1 . 6 10 C E1, y 9 109 2 3 8 C 2 10 m N E1, y 7.2 104 C Since r>>s: E1, y 200Å x 2Å 1 Using exact solution: 4 N E1, y 7.1999973 10 C 20 Interaction of a Point Charge and a Dipole Edipole F F F = QEdipole - 1 2qs =Q ,0,0 3 4pe 0 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 21 Dipole in a Uniform Field F = qE Forces on +q and –q have the same magnitude but opposite direction Fnet = + qE - qE = 0 What happens in this case? 22 Dipole in a Uniform Field F = qE Forces on +q and –q have the same magnitude but opposite direction Fnet = + qE - qE = 0 Dipole experiences a torque about its center of mass. What is the equilibrium position? Electric dipole can be used to measure the direction of electric field. 23 A Fundamental Rationale • If know E at some location, then we 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. 1 q1q2 F= rˆ 2 4pe 0 r q E= rˆ 2 4pe 0 r 1 v <<c !!! 24 Key Ideas in Chapter 14: Electric Field A charged particle makes an electric field at every location in space (except its own location). The electric field due to one particle affects other charged particles. The electric force on a charged particle is proportional to the net electric field at the location of that particle. The Superposition Principle: The net electric field at any lecation is the vector sum of the individual electric fields of all charge particles at other locations. The field due to one charged particle is not changed by the presence of other charged particles. An electric dipole consists of two particles with charges equal in magnitude and opposite in sign, separated by a short distance. Changes in electric fields travel at the speed of light ("retardation"). 25 iClicker 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. 26