Download Homework 5 - University of St. Thomas

HOMEWORK #5
Chapter 26: Magnetism: Force and Field
Page 461:
#3:A magnetic field points out of this page. Will a positively charged particle moving in the
plane of the page circle clockwise or counterclockwise as viewed from above?
#4: Do particles in a cyclotron gain energy from the electric field, the magnetic field or both?
#15: Find (a) the minimum magnetic field needed to exert a 5.4x10-15N force on an electron
moving 21x103m/s and (b) the field strength required if the field were at 45° to the electron’s
velocity.
#21: How long does it take to complete a circular orbit perpendicular to a 1.0G magnetic field?
#26: A wire carrying 15A makes a 25° angle with a uniform magnetic field. The magnetic force
per unit length of wire is 0.31N/m. Find (a) the magnetic field strength and (b) the maximum
force per unit length that could be achieved by reorienting the wire.
#32: What’s the current in a long wire if the magnetic field strength 1.2cm from the wire is 67µT?
Page 462:
#36: An electric motor contains a 250-turn circular coil 6.2cm in diameter. If it develops a
maximum torque of 1.2Nm at a current of 3.3A, what’s the field strength?
#37: The line integral of the magnetic field on a closed path surrounding a wire has the value
8.8µTm. Find the current in the wire.
#51: You’re designing a prosthetic ankle that includes a miniature electric motor containing a
150-turn coil 15mm in diameter. The motor needs to develop a maximum torque of 3.1mNm.
The strongest magnets available that will fit in the prosthesis produce 220mT field. What current
do you need in your motor’s coil?
Page 463:
#58: Your company is developing a device incorporating a 20-cm diameter coil carrying 0.5A
that, when properly oriented, will just cancel the Earth’s 50µT magnetic field at the coil’s center.
How much wire must you requisition for each coil?
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#80: Find an expression for the magnetic field at the center of a square loop of side a carrying a
current I.
Chapter 27: Electromagnetic Induction
Page 487:
#3: Fluctuations in the Earth’s magnetic field due to changing solar activity can wreak havoc with
communications, even those using underground cables. How is this possible?
#5: Can an induced electric field exist in the absence of a conductor?
#11: It takes work to push two bar magnets together with like poles facing. Where does this
energy go?
#12: Show that Volt is the SI unit for the rate of change of magnetic flux, making Faraday’s law
dimensionally correct.
#17: Find the self-inductance of a 1000-turn solenoid 50cm long and 4cm in diameter.
#28: The world’s strongest magnet that can produce a sustained field is a 45T device at the
National High Magnetic Field Laboratory in Florida. What’s the corresponding magnetic-energy
density?
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#30: The induced electric field 12cm from the axis of a 10-cm radius solenoid is 45V/m. Find the
rate of change of the solenoid’s magnetic field.
#34: A square wire loop of side l and resistance R is pulled with constant speed v from s region of
⃗
no magnetic field until it’s fully inside a region of constant, uniform magnetic field 𝐵
perpendicular to the loop plane. The boundary of the field region is parallel to one side of the
loop. Find an expression for the total work done by whatever is pulling the loop.
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#52: The current in a series RL circuit rises to half its final value in 7.6s. What’s the time constant?
#73: A long, straight coaxial cable consists of two thin tubular conductors, the inner of radius a and
the outer of radius b. Current I flows out along one conductor and back along the other. Find the
cable’s self-inductance per unit length.
Page 490:
#75: One way to measure blood flow when blood vessels are exposed during surgery is to use an
electromagnetic flowmeter. This device surrounds the blood vessel with an electromagnet, creating
a magnetic field perpendicular to the blood flow. Since blood is a modest conductor, a motional emf
develops across the blood vessel. Given vessel diameter d, magnetic field B, and voltage V
measured across the vessel, show that the volume blood flow is given by πd2V/4Bd.