Homework due tonight 11:59 PM Office hour today after class (3-4PM) in Serin 287 2 nd floor tea room or my office Serin 265 SUNDAY Nov 18: SECOND HOUR EXAM 6:10-7:30 PM in SEC 111 (Ch. 26-30) -- no recitations the previous Friday and following Monday
We ve been talking about the magnetic fields produced in systems with steady currents Biot-Savart law and Ampere s law Now back to electric fields If I have a system with fixed charge distribution, I know how to find the E-field Coulomb law and Gauss law Described by potential which depends on the charge dist Electric field is conservative work is path independent, zero around closed path Field lines cannot form closed loops If I add steady currents to the system of fixed charges, the electric fields don t change Electric field from charge, magnetic field from current
Clicker: True or false? A fixed charge distribution can produce the electric field shown in the figure. (a) true (b) false (c) not enough information to determine (d) I have no idea how to decide
Clicker: True or false? A fixed charge distribution can produce the electric field shown in the figure. (a) true (b) False electric field produced by fixed charge distribution is conservative field lines cannot form closed loops (c) not enough information to determine (d) I have no idea how to decide
Electric fields and fixed charges Coulomb s law d! E = k dq r 2 Gauss law closed surface Magnetic fields and steady currents Biot-Savart law ˆr S! E Ampere s law closed loop C d! A = q enc ε 0 What happens when charges and currents change with time?! B d! s = µ 0 i enc
The DEMO How can I get a current to flow in this coil? Insert a battery into the loop Potential difference across the ends Electric field along the wire + - I
The DEMO How can I get a current to flow in this coil? Current induced in a loop by a moving bar magnet Rate of motion Relative motion N/S towards/away
The DEMO How can I get a current to flow in this coil? Current induced in a loop by a moving bar magnet Rate of motion Relative motion N/S towards/away Changing magnetic field Verify: current induced in a loop by changing current in nearby loop
Electric field lines form a closed loop THIS NEVER HAPPENS IN ELECTROSTATICS! Changing magnetic field creates an electric field in addition to and DIFFERENT IN CHARACTER from that created by electric charges
New law that shows how CHANGES in magnetic field create this new kind of electric field FARADAY S LAW! E d s! = d! B d A! C S dt Iine integral surface integral (magnetic flux) Loop C is the boundary of the surface S
Magnetic flux through a surface Uniform magnetic field B Planar loop flat surface A, Flux = (B cosθ) A Units 1T m 2 = 1 Wb (weber) n ^
B(t) out of page increasing with time n ^ points out of page Φ = B(t)A dφ/dt is not zero Area 0.2 m 2 B(t) = (0.1T/s) t dφ/dt = 0.02 T m 2 /s Remember 1 T = 1 Ns /(Cm) dφ/dt = 0.02 Nm/C = 0.02 V
The boundary of the surface S is the closed loop C C! E d! s Direction for line integral if you walk along C with normal vector to surface as up, you should go the direction that keeps the surface on your left counterclockwise
B(t) out of page increasing with time C Φ = B(t)A dφ/dt! is not zero E d s! is not zero n ^ points out of page The current in the loop is not zero Bulb demo
B(t) out of page increasing with time n ^ points out of page Φ = B(t)A dφ/dt is not zero Area 0.2 m 2 B(t) = (0.1T/s) t dφ/dt = 0.02 V C! E d s! = -0.02 V E field loops clockwise
B(t) out of page increasing with time n ^ points out of page wire of resistance R made into a loop Φ = B(t)A dφ/dt is not zero Area 0.2 m 2 B(t) = (0.1T/s) t dφ/dt = 0.02 N m/c = 0.02V C! E d s! = -0.02V E field loops clockwise Current loops clockwise
C! E d! s = d dt S! B d! A The math is enough to figure out which way the E field is pointing around the loop OR Use Lenz s law to find direction of induced current: Any induced current would create an additional magnetic flux that OPPOSES dφ/dt
n ^ points out of page i Magnetic field inside the loop due to clockwise i is into the page Magnetic flux due to current in loop is negative
n ^ points out of page i Magnetic field inside the loop due to counterclockwise i is out of the page Magnetic flux due to current in loop is positive
B(t) out of page increasing with time wire of resistance R made into a loop n ^ points out of page i Φ = B(t)A Current flows in loop as if a battery were included E = -dφ/dt direction of induced current: current flowing in loop creates an additional magnetic flux that OPPOSES dφ/dt LENZ S LAW
B(t) out of page increasing with time wire of resistance R made into a loop n ^ points out of page i Φ = B(t)A Current flows in loop as if a battery were included E = -dφ/dt (walking counterclockwise) direction of induced current: current flowing in loop creates an additional magnetic flux that OPPOSES dφ/dt LENZ S LAW
clicker wire of resistance R made into a loop n ^ points out of page B(t) out of page and increasing with time Which direction does the induced current flow? (A) Clockwise (B) Counterclockwise (C) The current is zero The induced current produces a magnetic flux that OPPOSES THE CHANGE
clicker wire of resistance R made into a loop n ^ points out of page B(t) out of page and increasing with time Which direction does the induced current flow? (A) Clockwise (B) Counterclockwise (C) The current is zero The induced current produces a magnetic flux that OPPOSES THE CHANGE
clicker wire of resistance R made into a loop n ^ points out of page
Simplest way to change the flux Change the magnetic field Example 1: pass a bar magnet through the loop
Simplest way to change the flux Change the magnetic field Example 1: pass a bar magnet through the loop
Simplest way to change the flux Change the magnetic field Example 1: pass a bar magnet through the loop
Simplest way to change the flux Change the magnetic field Example 2: loop inside a solenoid with changing I Uniform field inside solenoid
Eddy currents The moving bar magnet may feel a force from the magnetic field produced by the induced current Galvanometer demo Falling magnet in copper tube (copper tube = stack of wire loops) The induced current may feel a force from the magnetic field Rolling disk demo, next time