Magnetic Fields VI Name: ____________________

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Magnetic Fields VI Name: ____________________
Magnetic Fields VI
Name: ____________________
# of problems you seriously attempted = _____
Magnetic Fields VI
Magnetic Fields VI
2. The figure shows two circular regions with radii R1 = 20 cm and R2 = 30 cm.
Everywhere within R1 there is a uniform magnetic field B1 = 50 mT out of the page, and
everywhere within R2 there is a uniform mangetic field B2 = 75 mT into the page. Both
fields are decreasing at a rate of 8.50 mT/s (i.e., this number equals –dB/dt). Calculate
the integral E   E  dl (which equals a voltage) for each of the three given paths.
Path 3
Path 2
R1
×
R2
Path 1
Magnetic Fields VI
3. In the figure, the magnetic field in the circular region increases
with time according to B = (2.00t3 - 4.00t2 + 0.800) Teslas, with r
= 2R = 5.00 cm. Calculate the magnitude and direction of the
force exerted on an electron located at point P at t = 2.00s.
P
×
×
F
× ×
×
× ×
×
× ×
×
×
r
×
R
Bin
Magnetic Fields VI
4. An electric field of 300 V/m is confined to a circular area 10.0 cm in diamter and
directed outward perpendicular to the plane of the fiugre. If the electric field is
increasing at a rate of 20.0 V/m·s, what are the direction and magnitude of the magnetic
field at point P, 15.0 cm from the center of the circle?
Magnetic Fields VI
HOMEWORK
1. Wolfson, Volume II, 2nd Edition, 27.30
2. Wolfson, Volume II, 2nd Edition, 27.49 (1 fN = 1 femtonewton = 10-15 N)
Magnetic Fields VI
3. MRI (magnetic resonance imaging) is very safe because it doesn’t deliver ionizing
radiation like x-rays do. One possible concern with MRIs is turning the magnetic field on
or off too quickly. Bodily fluids are conductors, and a changing magnetic field could
cause electric currents to flow through the patient. Suppose a typical patient has a
maximum cross-sectional area of 0.060 m2. What is the smallest time interval in which a
5.0T magnetic field can be turned on or off if the induced emf around the patient’s body
must be kept to less than 0.10 V? If the person’s cross-section is approximated as a circle,
what maximum electric field around the body’s perimeter corresponds to this emf?
4. Wolfson, Volume II, 2nd Edition, 29.13
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5. Wolfson, Volume II, 2nd Edition, 29.35
Magnetic Fields VI