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Moving electric charges ---- such as, current! Currents Create B fields - Ampere’s Law Magnitude: m0I B 2r Direction: RHR 2 Thumb in direction of current, fingers curl around current indicating direction of magnetic field r = distance from wire m0 = magnetic constant m 0 = 4 10-7 Tm/A B 1 B decreases as r r Current I OUT Lines of B When indicating direction of B by crosses and dots we always draw it like this. Note that the magnetic field lines form circles around the wire. Circles close to the wire have a stronger filed than those far away. I ● ● ● ● x x x x ● ● ● ● x x x x ● ● ● ● x x x x ● ● ● ● x x x x ● ● ● ● x x x x 1. What is the direction of the magnetic field at point A? a) b) c) d) Into the page Out of the page Up down A 2. What is the direction of the magnetic field at point B? a) b) c) d) Into the page Out of the page Up down 3. What is the shape of the magnetic field lines? a) circles b) spirals c) radially outward I B 4. Where is the magnetic field stronger? a) point A b) point B c) it’s the same at A and B q v • a) F B• v q • b) r F r I A long straight wire is carrying current from left to right. Near the wire is a charge q (-) with velocity v Compare magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) same B m0I 2r v and B are normal in both cases: sinθ= 1 same F = qvB F has different directions Adding Magnetic Fields Two long wires carry opposite currents I B ● I x I What is the direction of the magnetic field above, and midway between the two wires carrying current? 1) Left 2) Right 3) Up 4) Down 5) Zero Force between wires carrying current Current-carrying wires create magnetic fields Magnetic fields exert a force on current-carrying wires Current carrying wires exert forces on each other! Force between wires carrying current I up another I up F B F x B First, use RHR #2 to find the direction of the magnetic field on each wire. Then, use RHR #1 to find the force on each wire Conclusion: Currents in same direction attract! Let’s try another … another I down I up X F B Bx F Conclusion: Currents in opposite direction repel! What is the direction of the force on the top wire, due to the two below? 1) Left 2) Right 3) Up 4) Down 5) Zero What is the direction of the force on the middle wire, due to the two others? I 1) Left I 2) Right I 3) Up 4) Down 5) NoneZero What is the direction of the force on the left wire, due to the two others? I 1) Left I 2) Right I 3) Up 4) Down 5) None 5) Zero What is the direction of the force on the middle wire, due to the two others? I 1) Left 2I 2) Right 3I 3) Up 4) Down 5) None 5) Zero What is the direction of the force on the middle wire, due to the two others? I 1) Left I 2) Right I 3) Up 4) Down 5) None5) Zero What is the direction of the magnetic field on a point P in the middle of two wires? I I P What is the direction of the force on the left, due to the two others? I I I X 1) Left 2) Right 3) Up 4) Down 5) None) Zero 1) Left 2) Right 3) Up 4) Down 5) None 5) Zero Quick Review • How do you determine the direction of a magnetic field induced by a current? • How does magnetic field vary with distance from a wire? • What is the equation for induced magnetic field? • Opposite currents … • Currents in the same direction ... Quick Review • How do you determine the direction of a magnetic field induced by a current? RHR #2 – Thumb goes in direction of current, fingers curve in direction of mag. field • How does magnetic field vary with distance from a wire? Magnetic field decreases with distance m0I • What is the equation for induced magnetic field? B 2r • Opposite currents … repel • Currents in the same direction ... attract Solenoids A solenoid consists of several current loops stacked together. Used to create a strong, uniform magnetic field -- electromagnets -- starter for car engine B=μ0nI n = number of windings per unit length, I = current in windings B 0 outside windings