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Currents and Magnetism Textbook Sections 22-4 – 22-7 Physics 1161: Lecture 11

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Force of B-field on Current + v Force on 1 moving charge: –F = q v B sin( ) –Out of the page (RHR) Force on many moving charges: –F = (q/t)(vt)B sin( ) = I L B sin( ) –Out of the page! v L = vt B I = q/t ++++

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force is zero out of the page into the page B I L F=ILBsin Here = 0. A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A-B and C-D. What is the direction of the force on section A-B of the wire? Checkpoint Current Loop in Magnetic Field 1

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What is the direction of the force on section B-C of the wire? force is zero out of the page into the page A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides A- B and C-D. Palm into page. v F B X F Checkpoint Current Loop in Magnetic Field 2

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Net force on loop is zero. Look from here But the net torque is not! Torque on Current Loop in B field A B C D B I X F F A B C D F F The loop will spin in place! Checkpoint Current Loop in Magnetic Field 3 & 4

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Torque on loop is = 2 x (L/2) F sin( ) = Force on sections B-C and A-D: F = (length x width = area) LW = A ! Torque is = W L A B C D B I X F F Torque on Current Loop in B field A B C D F F

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Torque on loop is = 2 x (L/2) F sin( ) = ILWB sin( ) Force on sections B-C and A-D: F = IBW (length x width = area) LW = A ! Torque is = I A B sin( ) W L A B C D B I X F F Torque on Current Loop in B field A B C D F F L/2

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Torque tries to line up the normal with B! (when normal lines up with B, =0, so =0! ) Even if the loop is not rectangular, as long as it is flat: = I A B sin (area of loop) Magnitude: = I A B sin Direction: N # of loops A B C D B normal F F Torque on Current Loop between normal and B

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Compare the torque on loop 1 and 2 which have identical area, and current. 1 > 2 1 = 2 1 < 2

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Compare the torque on loop 1 and 2 which have identical area, and current. Area points out of page for both! = 90 degrees = I A B sin 1 > 2 1 = 2 1 < 2

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Currents Create B Fields Lines of B Current I OUT Right-Hand Rule-2 Thumb: along I Fingers: curl along B field lines r = distance from wire r Magnitude: B

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Right Hand Rule 2! wire I Fingers give B!

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θ is angle between v and B ( θ = 90° in both cases) 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 force is the same for (a) and (b) same B v I v (a) r r (b) F F Checkpoint Charge Moving Near Current

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Two long wires carry opposite current. What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? 1.Left 2.Right 3.Up 4.Down 5.Zero x x

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Two long wires carry opposite current. What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? 1.Left 2.Right 3.Up 4.Down 5.Zero x x B

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Force between current-carrying wires I towards us B Another I towards us F Conclusion: Currents in same direction attract! I towards us B Another I away from us F Conclusion: Currents in opposite direction repel! Note: this is different from the Coulomb force between like or unlike charges.

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Comparison: Electric Field vs. Magnetic Field ElectricMagnetic Source ChargesMoving Charges Acts on Charges Moving Charges Force F = Eq F = q v B sin( ) Direction Parallel EPerpendicular to v,B Field Lines Opposites Charges AttractCurrents Repel

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Checkpoint Solenoid A solenoid is wrapped with wire carrying a current, as shown in the figure. What is the direction of the magnetic field produced by the solenoid? a. into the right end of the solenoid and out of the left end b. out of the right end of the solenoid and into the left end

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Magnetic Fields of Currents http://hyperphysics.phy- astr.gsu.edu/hbase/magnetic/magfie.html#c1 http://hyperphysics.phy- astr.gsu.edu/hbase/magnetic/magfie.html#c1

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Right Hand Rule 3 Magnetic Field of Solenoid

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B Field Inside Solenoids Magnitude of Field anywhere inside of solenoid : B= 0 n I Right-Hand Rule for loop/solenoid Fingers – curl around coil in direction of conventional (+) current Thumb - points in direction of B along axis n is the number of turns of wire/meter on solenoid. = 4 x10 -7 T m /A (Note: N is the total number of turns, n = N / L) Magnetic field lines look like bar magnet! Solenoid has N and S poles!

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What is the force between the two solenoids? 1.Attractive 2.Zero 3.Repulsive

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What is the force between the two solenoids? 1.Attractive 2.Zero 3.Repulsive Look at field lines, opposites attract. Look at currents, same direction attract.

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The wires are separated by distance a and carry currents I 1 and I 2 in the same direction. Wire 2, carrying current I 2, sets up a magnetic field B 2.

The wires are separated by distance a and carry currents I 1 and I 2 in the same direction. Wire 2, carrying current I 2, sets up a magnetic field B 2.

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