Moving electric charges ---- such as, current!

Currents Create B fields - Ampere’s Law r = distance from wire  0 = magnetic constant Magnitude: Lines of B rB Current I OUT Direction: RHR 2 T humb in direction of current, fingers curl around current indicating direction of magnetic field B decreases as  0 = 4   T  m/A

x x x x ● ● ● ● I 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.

1.What is the direction of the magnetic field at point A? a)Into the page b)Out of the page c)Up d)down 2.What is the direction of the magnetic field at point B? a)Into the page b)Out of the page c)Up d)down 3.What is the shape of the magnetic field lines? a) circles a) circles b) spirals b) spirals c) radially outward c) radially outward I A B 4.Where is the magnetic field stronger? a) point A b) point B c) it’s the same at A and B

vB same v and B are normal in both cases: sinθ= 1 A long straight wire is carrying current from left to right. Near the wire is a charge q (-) with velocity v I v a) r q 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) c) force is the same for (a) and (b) q r b)F F F has different directions same F = qvB

Two long wires carry opposite currents I Two long wires carry opposite currents I What is the direction of the magnetic field above, and midway between the two wires carrying current? ● Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero B x II

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 B another I up F Conclusion: Currents in same direction attract ! x F I up B another I down F Conclusion: Currents in opposite direction repel! x F 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 Let’s try another … X B B

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? 1) Left 2) Right 3) Up 4) Down 5) NoneZero I II What is the direction of the force on the left wire, due to the two others? I II 1) Left 2) Right 3) Up 4) Down 5) None 5) Zero

What is the direction of the force on the middle wire, due to the two others? 1) Left 2) Right 3) Up 4) Down 5) None 5) Zero I 2I3I What is the direction of the force on the middle wire, due to the two others? I II 1) Left 2) Right 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? 1) Left 2) Right 3) Up 4) Down 5) None) Zero I P I What is the direction of the force on the left, due to the two others? I II 1) Left 2) Right 3) Up 4) Down 5) None 5) Zero X

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 What is the equation for induced magnetic field? 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=μ 0 nI n n = number of windings per unit length, I = current in windings B  0 outside windings