Download Chapter 27 Questions

Chapter 27 Questions
1. A proton moving with a speed of 4 x 106 m/s through a magnetic field of 1.7 T experiences a
magnetic force of magnitude 8.2 X 10-13 N. What is the angle between the proton’s velocity and
the field?
2. An electron is projected into a uniform magnetic field given by B = (1.4i + 2.1j) T. Find the
vector expression for the force on the electron when its velocity is v = 3.7 X 105j m/s.
3. A proton moves perpendicular to a uniform magnetic field B with a speed of 107 m/s and
experiences an acceleration of 2 x 1013 m/s2 in the +x direction when its velocity is in the +z
direction. Determine the magnitude and direction of the field.
4. A wire carries a steady current of 2.4 A. A straight section of the wire, with a length of 0.75 m
along the x axis, lies within a uniform magnetic field of magnitude B = (1.6k)T If the current
flows in the +x direction, what is the magnetic force on the section of wire?
5. A conductor suspended by two flexible wires as in shown has a mass per unit length of 0.04
kg/m. What current must exist in the conductor in order for the tension in the supporting wires to
be zero if the magnetic field over the region is 3.6 T into the page? What is the required direction
for the current?
6. A wire with a mass of 0.5 g/cm carries a 2-A current horizontally to the south. What are the
direction and magnitude of the minimum magnetic field needed to lift this wire vertically
upward?
7. A rectangular loop consists of 100 closely wrapped turns and has dimensions 0.4 m by 0.3 m.
The loop is hinged along the y-axis, and the plan of the coil makes an angle of 30° with the x
axis (as shown). What is the magnitude of the torque exerted on the loop by a uniform magnetic
field of 0.8 T directed along the x axis when the current in the windings has a value of 1.2 A in
the direction shown? What is the expected direction of rotation of the loop?
8. A rectangle coil of 225 turns and area 0.45 m2 is in a uniform magnetic field of 0.21 T.
Measurements indicate that the maximum torque exerted on the loop by the field is 8 X 10-3
N·m.
a) Calculate the current in the coil.
b) Would the value found for the required current be different if the 225 turns of wire were used
to form a single-turn coil with the same shape of larger area? Explain.
9. A circular coil of 100 turns has a radius of 0.025 m and carries a current of 0.1 A while in a
uniform external magnetic field of 1.5 T. How much work must be done to rotate the coil from
the position where the magnetic moment is parallel to the field to a position where the magnetic
moment is opposite the field?
10. A singly charged positive ion has a mass of 3.2 x10-26 kg. After being accelerated through a
potential difference of 833 V, the ion enters a magnetic field of 0.92 T along a direction
perpendicular to the direction of the field. Calculate the radius of the path of the ion in the field.
11. A cosmic-ray proton in interstellar space has an energy of 10 MeV and executes a circular
orbit with a radius equal to that of Mercury’s orbit around the Sun (5.8 X 1010 m). What is the
galactic magnetic field in that region of space?
12. A cyclotron designed to accelerate protons is provided with a magnetic field of 0.45 T and
has a radius of 1.2 m.
a) What is the cyclotron frequency?
b) What is the maximum speed acquired by the protons?
13. A wire with a mass of 1 g/cm is placed on a horizontal surface with a coefficient of friction
of 0.2. The wire carries a current of 1.5 A toward the east, and moves horizontally to the north.
What are the magnitude and the direction of the smallest magnetic field that enables the wire to
move in this fashion?
14. A positive charge q = 3.2 X 10-19 C moves with a velocity v = (2i+3j-k) m/s through a region
where both a uniform magnetic field and a uniform electric field exist.
a) Calculate the total fore on the moving charge (in unit-vector notation) if B = (2i+4j+k) T and
E = (4i-j-2k) V/m.
b) What angle does the force vector make relative to the positive x axis?
15. A metal rod having a mass per unit length of 0.010kg/m carries a current of I=5.0A. The rod
hangs from two vertical wires in a uniform vertical magnetic field as shown. If the wires make an
angle theta=45 degrees with the vertical when in equilibrium, determine the strength of the
magnetic field.