Magnetic Dipole in a Magnetic Field and the Biot-Savart Law Torque - PDF document

Magnetic Dipole in a Magnetic Field and the Biot-Savart Law � Torque on a Current Loop in a Uniform Magnetic Field � Magnetic Dipole in a Uniform Magnetic Field � The Biot-Savart Law � Magnetic Field on the Axis of a Circular Current Loop � Magnetic Field Lines � Homework

✤ ✠ ✠ ✥ ✤ ✠ ✆ ✆ ✒ ✠ ✆ ✑ ✏ ✠ ✝ ✁ ✆ ✁ ✄ ✆ ✁ ✟ Torque on a Current Loop Parallel to a Uniform Magnetic Field Serway/Jewett Figure 22.19 ✂✡✠ ✂☎✄ ✂✞✝ ☛✌☞✎✍ ✓✕✔✗✖ ✑✣✢ ✒✦✢ ✄✙✘ ✚✜✛

✖ ✢ ✆ ✤ ✢ ✩ ✤ ✥ ✩ ✆ Torque on a Current Loop Parallel to a Uniform Magnetic Field (cont’d) Serway/Jewett Figure 22.19 ✄✙✘ ✚✜✛ ✧★✓✕✔✗✖ ✧✪✓✕✔✫✖ ✄✙✘ ✚✜✛ ✓✭✬

✂ ✢ ✥ ✰ ✰✱ ✢ ✤ ✴ ✴ ✶ ✄ ✆ ✬ ✖ ✴ ✂ ✏ ✁ ✁ ✆ ✓ ✁ ✂ ✬ ✟ ✁ ✖ ✶ ✴ ✤ ✢ ✤ ✥ ✏ ✄ ✆ ✏ ✢ ✠ ✑ ✰ ✰✱ ✢ ✠ ✆ ✤ ✄ ✒ Torque on a Current Loop at an Angle to a Uniform Magnetic Field Serway/Jewett Figure 22.20 ☛✌☞✎✍ ☛✌☞✎✍ ☛✌☞✎✍ ✏✳✲✵✴ ☛✌☞✎✍ ✏✳✲✵✴ ✧★✓✕✔✗✖ ✩✯✮✰ ✧✷✓✕✔✗✖ ✩✸✮✰ ☛✌☞✹✍ ✓✕✔ ✂✺✄ is a vector perpendicular to the loop with a magni- tude equal to the area of the loop.

✂ ✂ ✂ ✁ ✬ ✁ ✑ ✆ ✁ ✬ ✁ ✁ ✓ ✾ ✟ ✁ ✁ ✂ ✖ ✁ ✻ Magnetic Dipole in a Uniform Magnetic Field ✂✼✻ � The magnetic dipole moment of the loop is de- fined as ✂✽✻ � The SI unit of magnetic dipole moment is the A ✿ m . � The direction of and is given by the right-hand rule. � So, the torque can be expressed as ✂✺✄ ✂✼✻ Serway/Jewett Figure 22.21

✝ ✁ ✑ ✆ ✝ ❈ ✟ ✟ ❀ ✻ ◆ ✬ ✆ ✖ ✂ ✁ ❀ ❁ The Biot-Savart Law Serway/Jewett Figure 22.22 ✻❂❁ ✂❇❆ ❃❅❄ ❉❋❊❍● ■❑❏ ❃❅❄ ✿▼▲ The constant is called the permeability of free space.

✑ ❀ ❙ ✁ ✂ ✖ ✆ ✖ ❲ ✖ ✛ ✆ ❳ ✖ ❆ ✆ ✻ ❁ ✓ ❳ ❀ ❆ ◗ ✑ ✥ ❙ ✑ ✥ ❀ ✝ ❀ ✖ ✆ ✻ ❁ ✓ ❖ ❀ ✁ ✂ ✟ ❈ ❆ ❖ ✆ ✓ ❁ ✑ ✻ ✝ ❀ ✖ Magnetic Field on the Axis of a Circular Current Loop Serway/Jewett Figure 22.24 ❃❅❄ ✑❯❚ P❘◗ ❃❅❄ ✛✗❱ ☛❫✏ ❨❪❩ ☛❭✏ ❨❬❩ ❃❅❄

✑ ❁ ✑ ❳ ❀ ❆ ✖ ✛ ✆ ✻ ✓ ✑ ❙ ✑ ✤ ✑ ✥ ❙ ✑ ❚ ❙ ✥ ✆ ❙ ✑ ✥ ❙ ✑ ✖ ✛ ✆ ✻ ❁ ✓ ❙ Magnetic Field on the Axis of a Circular Current Loop (cont’d) Serway/Jewett Figure 22.24 ☛▼✏ ❨❬❩ ✑❴❚❴❵❜❛ P✎◗ ✑❯❚❞❝❪❛ P✹◗ ❃❅❄ ❝❪❛ P✹◗

Magnetic Field Lines Serway/Jewett Figure 22.25 (a) and (c)

Homework Set 21 - Due Mon. May 24 � Read Sections 22.6 & 22.7 � Answer Questions 22.2, 22.11 � Do Problems 22.17, 22.18, 22.23, 22.24 & 23.27