Presentation on theme: "Today’s Concept: What Causes Magnetic Fields"— Presentation transcript:
1Today’s Concept: What Causes Magnetic Fields Physics 2112 Unit 14Today’s Concept:What Causes Magnetic Fields
2Compare to Electric Fields v out of the screenIn the same direction as r12Perpendicular to r12
3B field from one moving charge Biot-Savart LawB field from one moving chargeBut remember from previous slidesB field from tiny of current carrying wire.
4Example 14.1 (Infinite wire of current) What is the magnetic field a distance yo away from a infinitely long wire of current I?Conceptual PlanUse Biot-Savart LawStrategic AnalysisDone in prelecture in detailIntegrate(Similar to E field for infinite line of charge)Direction:Thumb: on IFingers: curl in direction of B
6Example 14.1 (answer)Magnitude:BCurrent I OUTr•Remember:
7Example 14.2 (B field from hexagon) A current, I, flows clockwise through a hexagonal loop of wire. The perpendicular distance between each side and the center of the loop is b.What is the magnetic field in the center of the loop?bQf
8Example 14.3 (From Loop)A current, I, flows clockwise through a circular loop of wire. The loop has a radius a.What is the magnetic field at a point P a distance yo above the plane of the loop in the center?PyoaxQBcosQQ
9Force Between Current-Carrying Wires I1X X X X X X X X X X X X X X X X X X XX X X X X X X X X X X X XX X X X X X X X X X X XX X X X X X X X X XFI2Maybe circle muI1/2pid as B?
10Force Between Current-Carrying Wires I towards usdB••Another I towards usFConclusion: Currents in same direction attract!•I towards usBdFAnother I away from usMaybe circle muI1/2pid as B?Conclusion: Currents in opposite direction repel!
11Example 14.4 (Two Current Carrying Wires) 50cmI2 = 10A10cmI1 = 5ATwo current carrying wires a 10cm apart for a length for 50cm. Wire 1 carries 5A and Wire 2 carries 10A with both current to the left.What is the magnitude and direction of the force on wire 2 due to wire 1?Draw B and F arrows
12CheckPoint 1AXBFWhat is the direction of the force on wire 2 due to wire 1?A) Up B) Down C) Into Screen D) Out of screen E) ZeroDraw B and F arrows
13CheckPoint 1BWhat is the direction of the torque on wire 2 due to wire 1?A) Up B) Down C) Into Screen D) Out of screen E) ZeroDraw B and F arrowsUniform force at every segment of wireNo torque about any axis
14What is the direction of the force on wire 2 due to wire 1? CheckPoint 3AWhat is the direction of the force on wire 2 due to wire 1?Up B) Down C) Into ScreenD) Out of screen E) Zero
15What is the direction of the torque on wire 2 due to wire 1? CheckPoint 3BWhat is the direction of the torque on wire 2 due to wire 1?Up B) Down C) Into ScreenD) Out of screen E) ZeroLET’S DRAW A PICTURE!
16Checkpoint 2: Force on a loop A current carrying loop of width a and length b is placed near a current carrying wire.How does the net force on the loop compare to the net force on a single wire segment of length a carrying the same amount of current placed at the same distance from the wire?the forces are in opposite directionsthe net forces are the same.the net force on the loop is greater than the net force on the wire segmentthe net force on the loop is smaller than the net force on the wire segmentthere is no net force on the loop
17Checkpoint questionCurrent flows in a loop as shown in the diagram at the right. The direction is such that someone standing at point a and looking toward point b would see the current flow clockwise.What is the orientation of the magnetic field produced by the loop at points a and b on the axis?(A)(B)(C)(D)
18B on axis from Current Loop ..IResulting B FieldCurrent in Wire
19Biot-Savart Works, but need to do numerically What about Off-Axis ?Biot-Savart Works, but need to do numericallySee Simulation!
20Two Current LoopsTwo identical loops are hung next to each other. Current flows in the same direction in both.The loops will:Attract each other B) Repel each otherC) There is no force between themNS2) Look like bar magnetsTwo ways to see this:1) Like currents attract
21Right Hand Rule Review 1. ANY CROSS PRODUCT 2. Direction of Magnetic MomentThumb: Magnetic MomentFingers: Current in Loop3. Direction of Magnetic Field from WireThumb: CurrentFingers: Magnetic Field
22Example 14.2yyTwo parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I = 1A flowing in the directions shown.What is the B field at point P?I1 = 1A.4cm3cmxz4cmPI2 = 1AFront viewSide viewConceptual AnalysisEach wire creates a magnetic field at PB from infinite wire: B = m0I / 2prTotal magnetic field at P obtained from superpositionThe purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.Strategic AnalysisCalculate B at P from each wire separatelyTotal B = vector sum of individual B fields
23If I = 6A, what is the magnitude of the magnetic field at point P? Example 14.5 (Curved Loop of Wire)If I = 6A, what is the magnitude of the magnetic field at point P?20cm12cmPConceptual PlanUse Biot-Savart LawStrategic AnalysisIntegrate both loopsNote straight sections cancel out.0 of 25039
24Remember how we used Gauss’ Law to avoid doing integral in E field? Good News!!!!!Remember how we used Gauss’ Law to avoid doing integral in E field?We got similar law for B fields!