Download Lecture 17: Electric Current and Magnetic Fields - Exam 2 Preparation and more Exams Physics in PDF only on Docsity! 1 Wed. Mar. 26, 2008 Physics 208, Lecture 17 1 Exam 2 covers Ch. 27-32, Lecture, Discussion, HW, Lab Chapter 27: Electric flux & Gauss’ law Chapter 29: Electric potential & work Chapter 30: Electric potential & field Chapter 28: Current & Conductivity Chapter 31: Circuits Chapter 32: Magnetic fields & forces (exclude 32.6,32.8,32.10) Exam 2 is Wed. Mar. 26, 5:30-7 pm, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308) Wed. Mar. 26, 2008 Physics 208, Lecture 17 2 Electric current produces magnetic field Current (flow of electric charges ) in wire produces magnetic field. That magnetic field aligns compass needle Current Magnetic field Wed. Mar. 26, 2008 Physics 208, Lecture 17 3 Law of Biot-Savart Each element of current produces a contribution to the magnetic field.r θ I ds ! dB = µ o 4" Ids# ˆ r r 2 B out of page dI dB r Wed. Mar. 26, 2008 Physics 208, Lecture 17 4 Magnetic field from long straight wire: Direction What direction is the magnetic field from an infinitely-long straight wire? I ! d r B = µ o 4" Id r s # ˆ r r 2 x y Wed. Mar. 26, 2008 Physics 208, Lecture 17 5 Current dependence How does the magnitude of the B-field change if the current is doubled? I ! d r B = µ o 4" Id r s # ˆ r r 2 x y A) Is halved B) Quadruples C) Stays same D) Doubles E) Is quartered Wed. Mar. 26, 2008 Physics 208, Lecture 17 6 Distance dependence How does the magnitude of the B-field at 2 compare to that at 1? I ! d r B = µ o 4" Id r s # ˆ r r 2 x y 1 2 A) B2=B1 B) B2=2B1 C) B2=B1/2 D) B2=4B1 E) B2=B1/4 2 Wed. Mar. 26, 2008 Physics 208, Lecture 17 7 Why? Biot-Savart says Why B(r)∝ 1/r instead of 1/r2 ? ! d r B = µ o 4" Id r s # ˆ r r 2 ! r r Large contribution from this current element. Decreases as 1/r2 I Small contribution from this current element. ~ independent of r Wed. Mar. 26, 2008 Physics 208, Lecture 17 8 Long straight wire All current elements produce B out of page x a ! r = x 2 + a 2 r θ! dB = µ o 4" Ids# ˆ r r 2 = µ o 4" I r 2 sin$ = µ o 4" I r 2 a r = µ o 4" I a x 2 + a2( ) 3 / 2 ! B = µ o Ia 4" dx x 2 + a2( ) 3 / 2 = #$ $ % µ o I 2"a Add them all up: Wed. Mar. 26, 2008 Physics 208, Lecture 17 9 Forces between currents Which of these pairs of currents will attract each other? A. A B. A & C C. B D. A & B A B C Wed. Mar. 26, 2008 Physics 208, Lecture 17 10 Force between current-carrying wires Attractive for parallel currents. Repulsive for antiparallel currents Wed. Mar. 26, 2008 Physics 208, Lecture 17 11 Field from a circular loop Each current element produce dB All contributions add as vectors Along axis, all components cancel except for x-comp Wed. Mar. 26, 2008 Physics 208, Lecture 17 12 Magnetic field from loop Which of these graphs best represents the magnetic field on the axis of the loop? Bz z x y Bz Bz Bz A. B. C. D. z z z z
