Today’s Concept: Faraday’s Law Lenz’s Law Physics 2112 Unit 17 Today’s Concept: Faraday’s Law Lenz’s Law

Define Magnetic Flux, FB The Plan Define Magnetic Flux, FB Introduce Faraday’s Law in terms of magnetic flux Do some examples to show how Faraday’s Law explains motional emf results we had last time.

Similar to electric flux FE Define FB Magnetic Flux: A B Similar to electric flux FE Think of FB as the number of field lines passing through the surface

Example 17.1 (Magnetic Flux) B 5cm A copper disk with radius 5cm is placed in a magnetic field of uniform strength 0.2T. What is the magnetic flux through the disk?

Notice Units: = T * m2 = N / C /(m/sec) * m2 = (V/m)/(m/sec) * m2 = V*sec

The emf will make a current flow if it can (like a battery). Faraday’s Law: In Words: When the flux FB through a loop changes, an emf is induced in the loop. The emf will make a current flow if it can (like a battery). I Magnetic fields alone don’t cause currents Changing magnetic fields cause currents

Three ways to change flux Faraday’s Law Three ways to change flux Change |A| Change |B| Change the angle between the two

Example 17.2 (Change |B|) A 10cm X 20m loop is formed by a motionless conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W. The entire apparatus is placed in a magnetic field that varies from 0 to 1.2 T in 30 seconds. x x x x x x x x B varies What is the current through the resistor?

Example 17.3 (Change Area) A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W. The entire apparatus is placed in a uniform magnetic field of 0.5 T pointing into the screen. x x x x x x x x The bar is pulled to the right by a force, F, at a velocity of 8m/sec. What is the current through the resistor?

17.4 (Change the angle) A 10cm X 20 cm loop is rotated at 10rev/sec in a magnetic field of 0.1T. If the loop is connected to a R = 50W resistor, what is the current?

Lenz’s Law In words: Whenever the magnetic flux through a surface changes a current is formed which creates a magnetic field which opposes that change.

CheckPoint 1 Suppose a current flows in a horizontal conducting loop in such a way that the magnetic flux produced by this current points upward. As viewed from above, in which direction is this current flowing?

CheckPoint 2 A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conducting loop is entering the field as shown. At the instant shown below left, what is the direction of the additional flux produced by the current induced in the loop?

CheckPoint 3 A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conducting loop is entering the field as shown. The upward flux through the loop as a function of time is shown by the blue trace. Which of the red traces below it best represents the current induced in the loop as a function of time as it passes over the magnet? (Positive means counter-clockwise as viewed from above):

Induced electric field is not conservative! A point of confusion…. Faraday’s Law: Note: Induced electric field is not conservative! 

Example 17.5 (Bar on Ramp) A square metal bar has a length of 1m and a mass 1.2kg and slides down between two legs of a conducting U shaped rail that is at an angle of 45o to the ground. Side view 45o . . . . . . . . Top view . . . . The entire rails/rod system has a resistance of 2.5W and is contained in a vertical 0.7T magnetic field. What is the maximum velocity of the rod?

Example 17.6 (solenoid) A long solenoid has 220 turns/cm and carries a current I=1.5A. It’s diameter is 3.2cm. At the center, we place a closely packed coil, C, with 32 turns that is 2.1cm in diameter. The current in the solenoid is reduced to zero in 25ms. What is the magnitude of the EMF induced in the coil while the current in the solenoid is changing?

Executive Summary: Faraday’s Law: where Executive Summary: emf → current → field a) induced only when flux is changing b) opposes the change

Remember?

A Change….. Electricity and magnetism are now connected!