#### Transcript Maxwell`s Equations

Maxwell’s Equations PH 203 Professor Lee Carkner Lecture 25 Transforming Voltage We often only have a single source of emf We need a device to transform the voltage Note that the flux must be changing, and thus the current must be changing Transformers only work for AC current Basic Transformer The emf then only depends on the number of turns in each e = N(DF/Dt) Vp/Vs = Np/Ns Where p and s are the primary and secondary solenoids Transformers and Current If Np > Ns, voltage decreases (is stepped down) Energy is conserved in a transformer so: IpVp = IsVs Decrease V, increase I Transformer Applications Voltage is stepped up for transmission Since P = I2R a small current is best for transmission wires Power pole transformers step the voltage down for household use to 120 or 240 V Maxwell’s Equations In 1864 James Clerk Maxwell presented to the Royal Society a series of equations that unified electricity and magnetism and light ∫ E ds = -dFB/dt ∫ B ds = m0e0(dFE/dt) + m0ienc ∫ E dA = qenc/e0 Gauss’s Law for Magnetism ∫ B dA = 0 Faraday’s Law ∫ E ds = -dFB/dt A changing magnetic field induces a current Note that for a uniform E over a uniform path, ∫ E ds = Es Ampere-Maxwell Law ∫ B ds = m0e0(dFE/dt) + m0ienc The second term (m0ienc) is Ampere’s law The first term (m0e0(dFE/dt)) is Maxwell’s Law of Induction So the total law means Magnetic fields are produced by changing electric flux or currents Displacement Current We can think of the changing flux term as being like a “virtual current”, called the displacement current, id id = e0(dFE/dt) ∫ B ds = m0id + m0ienc Displacement Current in Capacitor So then dFE/dt = A dE/dt or id = e0A(dE/dt) which is equal to the real current charging the capacitor Displacement Current and RHR We can also use the direction of the displacement current and the right hand rule to get the direction of the magnetic field Circular around the capacitor axis Same as the charging current Gauss’s Law for Electricity ∫ E dA = qenc/e0 The amount of electric force depends on the amount and sign of the charge Note that for a uniform E over a uniform area, ∫ E dA = EA Gauss’s Law for Magnetism ∫ B dA = 0 The magnetic flux through a surface is always zero Since magnetic fields are always dipolar Next Time Read 32.6-32.11 Problems: Ch 32, P: 32, 37, 44 How would you change R, C and w to increase the rms current through a RC circuit? A) B) C) D) E) Increase all three Increase R and C, decrease w Decrease R, increase C and w Decrease R and w, increase C Decrease all three How would you change R, L and w to increase the rms current through a RL circuit? A) B) C) D) E) Increase all three Increase R and L, decrease w Decrease R, increase L and w Decrease R and w, increase L Decrease all three How would you change R, L, C and w to increase the rms current through a RLC circuit? A) B) C) D) E) Increase all four Decrease w and C, increase R and L Decrease R and L, increase C and w Decrease R and w, increase L and C None of the above would always increase current