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Lesson 23
(1) For the surface in a magnetic field with the normal
chosen, find
1. the normal component of the magnetic field
2. the magnetic flux
(2) A rectangular wire frame of dimensions
10cm×20cm is in a uniform magnetic field of 4.00G in
the x-direction. Find the magnetic flux if the normal
vector is
ˆ
i
(a)
(b) ĵ
ˆ
ˆ

i

j
(c)
2
(3) Find the magnetic flux through the triangle abc
where the magnetic field is 2.0T in the +z direction.
(4) A circular wire of radius 0.6m and resistance 50Ω
is on a plane perpendicular to a uniform magnetic
field. The magnetic field increases from 1.0T to 3.0T
in 5.0ms. Choosing the normal parallel to the
magnetic field, find
1. the change of magnetic flux
through the wire loop
2. the magnitude and direction
of the averaged induced emf
3. the averaged current
through the wire
4. the electric field inside the wire
(5) The loop of the previous problem is flipped
through 180° in 2.0s while the magnetic field stays
contant at 1.0T. Find
1. the averaged induced emf
2. the total charge that has circulated through the
loop during this time.
(6) The magnetic flux through a coil rotating in a
magnetic field is given by
1
jm =
cos100p t Wb
50p
where t is in seconds. Find the induced emf at
t=0.005s.
(7) A metal ring is falling away from a magnet. When
viewed from the bottom as shown, is the induced
current clockwise or counter-clockwise?
(8) A small circular loop is concentric with a large
circular loop. A current flows in the large loop in the
counterclockwise direction, and is diminishing. Use
Lenz law to determine the direction of the induced
current in the small loop.
(9) Refer to the previous problem. The radius of the
large loop is 50cm and that of the small loop is 1.0
cm. The current in the large loop reduces from 10.0A
to 4.0A in a 30ms interval. What is the induced emf in
the small loop during this time interval? (Hint: the
magnetic field due to the large loop at the small loop
can be considered uniform)