Phy2049: Magnetism Last lecture: Biot-Savart’s and Ampere’s law: –Magnetic Field due to a straight wire –Current loops (whole or bits)and solenoids Today: reminder and Faraday’s law.

hitt Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as shown. They each carry 3A but in the opposite direction. The wire on the left has the current coming out of the paper while the wire on the right carries the current going into the paper. The magnetic field at the third vertex (P) has the magnitude and direction (North is up): (1) 20 μT, east (2) 17 μT, west (3) 15 μT, north (4) 26 μT, south (5) none of these X 4 cm

Magnetic Field Units From the expression for force on a current-carrying wire: –B = F max / I L –Units: Newtons/A  m  Tesla (SI unit) –Another unit: 1 gauss = Tesla Some sample magnetic field strengths: –Earth: B = 0.5 gauss = 0.5 x T = 5 x T –Galaxy: B  gauss = T –Bar magnet: B  100 – 200 gauss –Strong electromagnet: B = 2 T –Superconducting magnet: B = 20 – 40 T –Pulse magnet: B  100 T –Neutron star: B  10 8 – 10 9 T –Magnetar: B  T

Force Between Two Parallel Currents Force on I 2 from I 1 –RHR  Force towards I 1 Force on I 1 from I 2 –RHR  Force towards I 2 Magnetic forces cause attraction between two parallel currents I1I1 I2I2 I1I1 I2I2

Force Between Two Anti-Parallel Currents Force on I 2 from I 1 –RHR  Force away from I 1 Force on I 1 from I 2 –RHR  Force away from I 2 Magnetic forces repel two antiparallel currents I1I1 I2I2 I1I1 I2I2

Parallel Currents (cont.) Look at them edge on to see B fields more clearly Antiparallel: repel F F Parallel: attract F F B B B B

B Center of Circular Current Loop Radius R and current i: find B field at center of loop –Direction: RHR #3 (see picture) If N turns close together

Current Loop Example i = 500 A, r = 5 cm, N=20 Challenge: How much heat is produced?

B Field of Solenoid Formula found from Ampere’s law –i = current –n = turns / meter –B ~ constant inside solenoid –B ~ zero outside solenoid –Most accurate when L>>R Example: i = 100A, n = 10 turns/cm –n = 1000 turns / m

Field at Center of Partial Loop Suppose loop covers angle  Use example where  =  (half circle) –Define direction into page as positive

Partial Loops (cont.) Note on problems when you have to evaluate a B field at a point from several partial loops –Only loop parts contribute, proportional to angle (previous slide) –Straight sections aimed at point contribute nothing –Be careful about signs, e.g.in (b) fields partially cancel, whereas in (a) and (c) they add

(29 – 14)

Chapter 30 Induction and Inductance In this chapter we will study the following topics: -Faraday’s law of induction -Lenz’s rule -Electric field induced by a changing magnetic field Electric current without a battery -Inductance and mutual inductance - RL circuits -Energy stored in a magnetic field (30 – 1)

(30 – 2)

loop 1 loop 2 (30 – 3)

(30 – 4)

loop (30 – 5)

(30 – 6)

NS magnet motion (30 – 7)

N S magnet motion (30 – 8)

S N magnet motion (30 – 9)

S N magnet motion (30 –10)

(30 –11)

(30 –12)

(30 –13)

(30 –14)

(30 –15)

(30 –16)

loop 1 loop 2 (30 –17)

(30 –19)

(30 –20)

(30 –21)

N2N2 N1N1 (30 –22)

N2N2 N1N1 (30 –23)

N2N2 N1N1 (30 –24)

Electrons are going around a circle in a counterclockwise direction as shown. At the center of the circle they produce a magnetic field that is: A. into the page B. out of the page C. to the left D. to the right E. zero e

Long parallel wires carry equal currents into or out of the page. Rank according to the magnitude of the net magnetic field at the center of the square, highest first. (Parenthesis means the same magnitude). 1. C,D, (A,B)2. A, B, (C,D)3. B, A, C, D 4. D, (A, B), C

Long, straight, parallel wires carry equal currents into or out of page. Rank according to the magnitude of the force on the central wire. 1. d, c, a, b 2. a, b, c, d3. b, c, d, a4. c, a, b, d 5. b, d, c, a