Magnetic Fields VI Name: ____________________

Magnetic Fields VI
Name: ____________________
# of problems you seriously attempted = _____
Magnetic Fields VI
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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
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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
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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?
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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
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