Electromagnetic Induction Current Induced in a Straight Conductor - PDF document

Electromagnetic Induction � Current Induced in a Straight Conductor � Current Induced in a Loop of Wire � Faraday’s Law of Induction � Magnetic Flux � Lenz’s Law � Homework

✟ ✂ ☎ ✂ ✄ ✂ Current Induced in a Straight Conductor ✄✆☎ ✁ moves with velocity � A conductor of length ✄✞✝ through ✠ perpendicular to a uniform magnetic field . � A current is induced in the conductor due to the magnetic force on charges in the conductor. Serway/Jewett Figure 23.1

Current Induced in a Loop of Wire � A current is induced in the loop when a magnet is moved toward the loop. � No current is induced in the loop when the magnet is stationary. � When the magnet is moved away from the loop. A current is induced in the opposite direction. Serway/Jewett Figure 23.2

✂ ☛ ✔ ✘ ✂ ✡ ☞ ✂ ☛ ✗ ✎ ✂ ✂ ☛ ✡ ✘ ✎ ☞ Faraday’s Law of Induction � The induced emf in a circuit is equal (except for a negative sign) to the rate at which the magnetic flux through the circuit changes with time. ☞✍✌ ✄✞✝ ✄✖✕ ☞✑✏ ☞✑✏✓✒ � The SI unit of magnetic flux is the weber (Wb): 1 Wb = 1 T.m � The negative sign is an indication of the direction of the induced emf. � When applying Faraday’s law to a coil with turns, an emf appears in every turn and these emfs add. ☞✍✌ ☞✑✏

✂ ✝ ✕ ✎ ✄ ✂ ☞ ✂ ☞ ✕ ✂ ✄ ✝ ✔ ☞ ☞ Magnetic Flux ☞✍✌ � The magnetic flux ✄✖✕ ✄✙✕ ✚✜✛✣✢✥✤ through a differential ele- ment of area is given by = . � Note that the vector is perpendicular to the sur- face. Serway/Jewett Figure 23.4

● ✏ ✎ ✌ ☛ ✎ ✌ ● ❋ ✗ ❉ ✂ ☛ ☛ ✗ ✳ ✱ ✱ ✂ ✯ ◆ ❍ ✌ ✭ ✌ ❋ ✗ ❊ ✘ ❉ ● ✂ ☛ ✎ ● ✎ ❋ ✗ ✌ ❉ ✎ ✂ ✺ ☛ ✦ ✮ ✭ ☛ ✄ ✟ ✝ ✒ ☛ ☛ ✂ ☞ ✵ ✝ ✂ ✕ ✒ ☛ ❋ ✌ ✾ ✡ ☛ ✡ ☛ ☞ ☛ ✬✭ ✱ ✪ ✾ ✂ ☛ ❉ ✌ ✗ ✳ ✱ ❊ ✝ ✯ ☞ ✭✮ ✭ ✬✭ ✗ ✝ ☛ ✡ ✂ Example A 1000-turn coil is 10.0 cm in diameter. What emf is developed across the coil if the magnetic field through the coil is reduced from 6.00 T to 0.00 in (a) 1.00 s, (b) 0.100 s, and (c) 0.100 ms? dA B i ✰✲✱ ✟★✔ ✄✙✕ ✟✩✕ ✟✫✪ ✎✧✦ ✰✲✱ ✺✹✸❀✿❁✺✣✺❃❂ ✎✴✦ ✵✷✶✹✸✻✺✣✺✽✼ ❄❅✸❇❆❈✿ ✿❁✺✑❊ ❄❅✸❇❆❈✿ ✿❁✺✑❊ ❄❅✸❇❆❈✿ ✿❁✺ ❄❅✸❇❆❈✿ ✿❁✺ ❋P❖ ✵✷■❏✾❑✡ ✵▲✿❁✺✣✺✣✺▼✾ ✿✣✸✻✺✣✺❘◗ ❄❙❆❈✸❚✿❱❯ ❄❙❆❈✿❱❯ ✵❳❲❨✾ ❄❙❆❈✿❱❩❬❯

Lenz’s Law � The induced current will appear in such a direction that it opposes the change that produced it. � That is, the induced current is in a direction such that the induced magnetic field attempts to maintain the original flux through the loop. Serway/Jewett Figure 23.16

Homework Set 23 - Due Fri. May 28 � Read Sections 23.1 & 23.3 � Answer Question 23.1 � Do Problems 23.1, 23.3 & 23.6