This Set o Slides - Day 20, Friday, Feb 19

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1 This Set o Slides - Day 20, Friday, Feb 19 Magnetic Field of Moving Charge or Current Biot-Savart Law Cross Product. Biot-Savart Law as cross product. More right hand rules. Three total! Similar but different!

2 Day 20, Friday, Feb 19, Announcement(s) Five days from tonight is the second exam. 8:30-9:50. Exam 2 covers Chapters (elec pot thru circuits.) Make your own equation sheet (as exam 1.) All students in this section will take their exam in: Learning Innovation Center (LINC) 228 MIDTERM 2 HELP/STUDY SESSION: Saturday, Feb 20, 2016, 2-5:00 pm, in Weniger 212.

3 Magnetic Field Due to a Long, Current-Carrying Wire The magnitude of the magnetic field at a perpendicular distance r away from the long wire is found via: B = μ 0 I / (2 π r) B = magnetic field strength. SI units will be the tesla (T). μ 0 = permeability of free space constant = 4π x10-7 T m/a = 1.257x10-6 T m/a I = current in amperes r = radial distance from the wire to the point where the field strength is computed (in meters). The direction of the field is the direction as determined from a right hand rule.

4 Examples A long wire that carries 3.0 A current is parallel to a long wire carrying 5.0 A current. If the wires are separated by 4.0 cm, where along a (perpendicular) line joining the two wires (the x-axis for example) is the magnetic field zero if the currents are a) in the same direction? b) in opposite directions? Loop plus wire. What is the B field magnitude and direction at point P?

5 Biot-Savart Law Magnetic field due to a moving charge: B = {[μ 0 / (4π)] [q v sin θ / r 2 ], RHR direction} B = magnetic field. SI units will be the tesla (T). 1 T = 1 N / A m μ 0 = permeability of free space constant = 4π x10-7 T m/a q = charge in coloumbs v = speed charge is moving r = distance from the charge to the point where the field is computed θ = angle between v and r

6 The Cross Product = (CD sin, direction given by the right-hand rule) Slide 32-52

7 As a vector equation: Biot-Savart Law Again B = magnetic field. SI units will be the tesla (T). μ 0 = permeability of free space constant = 4π x10-7 T m/a q = charge in coloumbs v = velocity of charge r-hat = unit vector pointing from the charge to the point where the field is being computed. r = distance from the charge to the point where the field is computed

8 Magnetic Field Direction Slide 32-53

9 Biot-Savart Law Yet Again For a short chunk o current: I = current (in amperes) Δs = length of short segment

10 Magnetic Field of a Long, Straight Wire Redux Use Biot-Savart s Law to find the field around a very long wire. Set wire along x-axis. Find field at x=0, y=d. Right hand rule to help out! Sort out geometry of cross product. Sum over all segments an infinite number of em. Integration! Integrate from neg. infinity to pos. infinity. Back where we were earlier but now you know why!

11 Magnetic Field Due to Current-Carrying Loop o Wire If we take that long, straight, current-carrying wire and bend it around into a circular loop, we get a concentration of the magnetic field at the center of the loop. The magnitude of the magnetic field at the center of loop: B = μ 0 I / (2 R) B = magnetic field strength. μ 0 = permeability constant = 4π x10-7 T m/a I = current in amperes R = radius of loop (in meters)

12 Magnetic Field Due to Many Loops o Wire If we loop that wire around N times, the magnetic field will be N times stronger. The magnitude of the magnetic field at the center of a thin coil of N loops: B = μ 0 N I / (2 R) B = magnetic field strength. μ 0 = permeability constant = 4π x10-7 T m/a N = number of loops/turns I = current in amperes R = radius of loop (in meters)

13 Right Hand Rule Again, plus a Variant The direction of the magnetic field at the center of a current-carrying loop (or loops) of wire can be found by the first right-hand rule we did a bit ago. Not to confuse the issue, but, another possible right hand rule for loops of wire and solenoids. Curl and point your fingers in the direction of the current in the loop or solenoid; that is, grab the loop or solenoid so your fingers point in the direction of the current. Your sticking-out thumb will point in the direction of the field, in the direction of the north pole of the created magnetic field, at the center of the loop or solenoid.

14 The Magnetic Field of a Current Loop Slide 24-34

15 Example with loop Loop plus wire. What is the B field magnitude and direction at point P?

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