1. Phy2005
Applied Physics II
Spring 2017
Announcements:

2. (dB/dt) rate of ch of B with time
Last Time
(& time before last)
Faraday’s law: any time there is a time-changing magnetic flux through
an area, there is an electromotive force (voltage) tending to drive
current around the boundary of the area
Vind = - A
(dB/dt) rate of ch of B with time
= - d/dt (rate of ch of  with time)
 = BA= B A : magnetic flux
Sign in Faraday’s law – “Lenz’s law”
Current flows in a direction so as to oppose the change in flux it experiences

3. Magnet always feels resistance to its motion.
Last time: practice w/ Faraday
Magnet always feels resistance to its motion.

5. Demos
Earth field generator
Faraday’s law with diode

6. q B -1.1×10-4 V 8 x 10-5 T -4 x 10-5 T-m2 4 x 10-1 T-m2 q
Q1. ( 23.7) A flat loop of wire has an
area of m2. It is in a region where
B=0.02 T and directed along the x axis.
is the angle between the normal of the loop
and the x axis. The loop is rotated from
q=0o to q=60o in 0.5s. What is the change in flux? B B q
dF = BfA-BiA = BAcos qf-BAcos qi)
= (0.02)(0.004)(1/2 – 1)
= -4 x 10-5 T-m2
-1.1×10-4 V
8 x 10-5 T
-4 x 10-5 T-m2
4 x 10-1 T-m2 q B

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8. Q2. ( 23.7) A flat loop of wire has an
area of m2. It is in a region where
B=0.02 T and directed along the x axis.
is the angle between the normal of the loop
and the x axis. The loop is rotated from
q=0o to q=60o in 0.5s. What is the induced EMF?
1.1×10-4 V
8 x 10-5 V
4 x 10-5 V
1.1 x 10-1 V q B

9. Ex A circular loop with a 10 cm-radius is placed in the presence of a uniform magnetic as shown in the figure. The field changes from 1.5 T to 0.5 T in 0.5 s. The loop has resistance 10W. What is the induced EMF? What current flows (specify the direction and magnitude)?
Vind = -d/dt
d = f - I = Tm2
Vind = V
I = Vind/R = Amp
Field B out of screen

10. Motional emf Fi = LdB Ff = L(d+vdt)B Vind = - dF/dt = - LvdtB/dt
x x x x x x L v
V dt d
Fi = LdB Ff = L(d+vdt)B
Vind = - dF/dt
= - LvdtB/dt
= - LvB

11. One way to think about it: electrons
In wire experience Lorentz force downwards - B
x x x x x x L v
Current flows counterclockwise; electrons flow clockwise
Vind = - B dA/dt = B (vdt)L/dt = BvL

12. 23-30 HW challenge: sliding
wire (no friction) on inclined rails.
Rails are resistanceless, but
wire has resistance R. What is
the terminal velocity?
Q1:Observation: wire slides down, accelerating until it
reaches a terminal velocity. Why????
A1: Because induced emf causes counterclockwise current,
sliding wire experiences increasing force component up the
rails, counteracting gravity
Q2: Total mechanical energy not conserved, since KE is const
and PE decreasing --- where is energy going?
A2: into heat dissipated in the resistor

13. Newton’s 2nd law: balance forces
Fwire cos a
Iind
Fwire
mg sin a mg