29. Sources of Magnetic Field

The on-axis magnetic field strength 10 cm from a small bar magnet is 500 μT. What is the on-axis field strength 15 cm from the magnet?

Which of the following is responsible for generating the magnetic field that surrounds a straight wire carrying an electric current?

CALC An 8.0 cm×8.0 cm square loop is halfway into a magnetic field perpendicular to the plane of the loop. The loop's mass is 10 g and its resistance is 0.010 Ω. A switch is closed at t = 0 s, causing the magnetic field to increase from 0 to 1.0 T in 0.010 s. Hint: What is the impulse on the loop? With what speed is the loop 'kicked' away from the magnetic field?

Which of the following is responsible for generating the magnetic field around a straight, current-carrying wire?$$

Jumper cables used to start a stalled vehicle often carry a 65-A current. How strong is the magnetic field 5.0 cm from one cable? Compare to the Earth’s magnetic field (5.0 x 10⁻⁵ T).

(II) Two long thin parallel wires 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field vector at a point 10.0 cm from one wire and 6.0 cm from the other (Fig. 28–37). [Hint: You could try using the law of cosines, Appendix A.]

A long straight wire carrying a current $I$ is placed parallel to one side of a rectangular current loop carrying current $I\text{'}$. If the distance between the wire and the nearest side of the loop is $d$, in which direction is the net force on the loop due to the magnetic field produced by the straight wire?

(II) Two long wires are oriented so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. 28–42). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 18.0 A and the bottom one carries 12.0 A?

A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at x = -2.0 cm. A second, parallel wire carrying a 3.0 A current intersects the x-axis at x = +2.0 cm. At what point or points on the x-axis is the magnetic field zero if (a) the two currents are in the same direction and (b) the two currents are in opposite directions?

What are the magnetic fields at points a to c in FIGURE EX29.13? Give your answers as vectors.

(II) In Fig. 28–36, a long straight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction and (relative) magnitude of $\overrightarrow{B}$ at each of the points C, D, and E in the plane of the page.

Determine the magnetic field at a point P due to a very long wire with a square bend as shown in Fig. 28–63. The point P is halfway between the two corners.

(II) Consider a straight section of wire of length d, as in Fig. 28–51, which carries a current I. (a) Show that the magnetic field at a point P a distance 𝑅 from the wire along its perpendicular bisector is

$B=\frac{{\mu }_{0}I}{2\pi R}\frac{d}{(d^2+4R^2{)}^{\frac{1}{2}}}$

(b) Show that this is consistent with Example 28–10 for an infinite wire.