# Lect08 - Force on a Current F = q v B sin Force due to...

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1 Force due to Magnetic Fields on Currents (Lorentz Force) Change in Magnetic Flux creates EMF (Faraday’s Law) 10/3/11 Physics 104, Fall 2011 1 Force on a Current F = q v B sin( θ ) Out of the page (RHR) 10/3/11 Physics 104, Fall 2011 2 + v F =(q/t)(vt)B sin( θ ) = I L B sin( θ ) Out of page θ + v L = vt B I = q/t + + + B 10/3/11 Physics 104, Fall 2011 3 Force between wires carrying current 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. B = μ 0 I 1 2 π d F = BI 2 l = μ 0 I 1 2 π d I 2 l Force per unit length, F l = μ 0 I 1 I 2 2 π d Magnetic Force Between Two Parallel Conductors The force on wire 1 is due to the current in wire 1 and the magnetic field produced by wire 2 The force per unit length is: 10/3/11 Physics 104, Fall 2011 4 F = μ o I 1 I 2 2 π d 10/3/11 Physics 104, Fall 2011 5 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 Electric and Magnetic Field 10/3/11 Physics 104, Fall 2011 6 Electric Magnetic Source: Charges Moving Charges Act on: Charges Moving Charges Magnitude: F=qE F = q v B sin( θ ) Direction: Parallel E Perpendicular to v,B Direction: Opposites Charges Attract Currents Repel

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2 10/3/11 Physics 104, Fall 2011 7 We have found the direction of F on each section of the loop. How about the magnitude? Torque on loop is τ = L F sin( ϕ ) = I LW B sin( ϕ ) F a b c d B I X F W L a b c d F F L B I W θ F= I B Wsin θ θ =90º On b-c and a-d sections F = I B W The area of the loop is A = WL ϕ torque is τ = I A B sin( ϕ ) φ Torque on Rotated Loop 10/3/11 Physics 104, Fall 2011 8 a b c d B normal = μ φ The torque tries to line up the normal with B ! Even if the loop is not rectangular, as long as it is flat ( area ) Magnitude Direction: N = # of loops F F τ = IAB sin φ τ = μ B sin φ = NIA ( ) B sin φ Torque on Rotated Loop What is the torque on the loop below?
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