1. Active Figure 29.1 Compass needles can be used to trace the magnetic field lines in the region outside a bar magnet.

2. Figure 29.3 The direction of the magnetic force FB acting on a charged particle moving with a velocity v in the presence of a magnetic field B. (a) The magnetic force is perpendicular to both v and B. Henry Leap and Jim Lehman

3. Figure 29.4 Two right-hand rules for determining the direction of the magnetic force FB q v B acting on a particle with charge q moving with a velocity v in a magnetic field B. (a) In this rule, the fingers point in the direction of v, with B coming out of your palm, so that you can curl your fingers in the direction of B. The direction of B, and the force on a positive charge, is the direction in which the thumb points. (b) In this rule, the vector v is in the direction of your thumb and B in the direction of your fingers. The force F on a positive charge is in the direction of your palm, as if you are pushing the particle with your hand.

4. Figure 29.6 (a) Magnetic field lines coming out of the paper are indicated by dots, representing the tips of arrows coming outward. (b) Magnetic field lines going into the paper are indicated by crosses, representing the feathers of arrows going inward.

5. Active Figure When the velocity of a charged particle is perpendicular to a uniform magnetic field, the particle moves in a circular path in a plane perpendicular to B. The magnetic force FB acting on the charge is always directed toward the center of the circle.

6. Active Figure A charged particle having a velocity vector that has a component parallel to a uniform magnetic field moves in a helical path.

7. Active Figure 29. 23 (a) A velocity selector
Active Figure (a) A velocity selector. When a positively charged particle is moving with velocity v in the presence of a magnetic field directed into the page and an electric field directed downward, it experiences a downward electric force qE and an upward magnetic force q v B. (b) When these forces balance, the particle moves in a horizontal line through the fields.

8. Active Figure 29. 24 A mass spectrometer
Active Figure A mass spectrometer. Positively charged particles are sent first through a velocity selector and then into a region where the magnetic field B0 causes the particles to move in a semicircular path and strike a detector array at P.

9. Figure 29.7 (a) A wire suspended vertically between the poles of a magnet. (b) The setup shown in part (a) as seen looking at the south pole of the magnet, so that the magnetic field (blue crosses) is directed into the page. When there is no current in the wire, it remains vertical. (c) When the current is upward, the wire deflects to the left. (d) When the current is downward, the wire deflects to the right.

10. Figure 29.8 A segment of a current-carrying wire in a magnetic field B. The magnetic force exerted on each charge making up the current is q vd B and the net force on the segment of length L is I L B.

11. Figure 29.9 A wire segment of arbitrary shape carrying a current I in a magnetic field B experiences a magnetic force. The force on any segment ds is I ds B and is directed out of the page. You should use the right-hand rule to confirm this force direction.

12. Figure (a) Overhead view of a rectangular current loop in a uniform magnetic field. No forces are acting on sides and because these sides are parallel to B. Forces are acting on sides and , however. (b) Edge view of the loop sighting down sides and shows that the forces F2 and F4 exerted on these sides create a torque that tends to twist the loop clockwise. The purple dot in the left circle represents current in wire coming toward you; the purple cross in the right circle represents current in wire moving away from you.

13. Active Figure 29. 14 An end view of the loop in Figure 29
Active Figure An end view of the loop in Figure 29.13b rotated through an angle with respect to the magnetic field. If B is at an angle with respect to vector A, which is perpendicular to the plane of the loop, the torque is IAB sin where the magnitude of A is A, the area of the loop.

14. Figure Right-hand rule for determining the direction of the vector A. The direction of the magnetic moment is the same as the direction of A.

15. Figure 30.1 The magnetic field dB at a point due to the current I through a length element ds is given by the Biot–Savart law. The direction of the field is out of the page at P and into the page at P.

16. Figure 30.4 The right-hand rule for determining the direction of the magnetic field surrounding a long, straight wire carrying a current. Note that the magnetic field lines form circles around the wire.

17. Active Figure 30.8 Two parallel wires that each carry a steady current exert a force on each other. The field B2 due to the current in wire 2 exerts a force of magnitude F1 I1B2 on wire 1. The force is attractive if the currents are parallel (as shown) and repulsive if the currents are antiparallel.

18. Active Figure 30.9 (a) When no current is present in the wire, all compass needles point in the same direction (toward the Earth’s north pole). (b) When the wire carries a strong current, the compass needles deflect in a direction tangent to the circle, which is the direction of the magnetic field created by the current. (c) Circular magnetic field lines surrounding a current-carrying conductor, displayed with iron filings.

19. Figure (a) Magnetic field lines for a tightly wound solenoid of finite length, carrying a steady current. The field in the interior space is strong and nearly uniform. Note that the field lines resemble those of a bar magnet, meaning that the solenoid effectively has north and south poles.

20. Figure Cross-sectional view of an ideal solenoid, where the interior magnetic field is uniform and the exterior field is close to zero. Ampère’s law applied to the circular path near the bottom whose plane is perpendicular to the page can be used to show that there is a weak field outside the solenoid. Ampère’s law applied to the rectangular dashed path in the plane of the page can be used to calculate the magnitude of the interior field.

21. Figure An electron moving in a circular orbit of radius r has an angular momentum L in one direction and a magnetic moment in the opposite direction.

22. Figure (a) Random orientation of atomic magnetic dipoles in the domains of an unmagnetized substance. (b) When an external field B0 is applied, the domains with components of magnetic moment in the same direction as B0 grow larger, giving the sample a net magnetization. (c) As the field is made even stronger, the domains with magnetic moment vectors not aligned with the external field become very small.