Currents and Magnetism Textbook Sections 22-4 – 22-7 Physics 1161: PreLecture 13

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 ++++

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!

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

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

Currents Create B Fields Lines of B Here’s a current- carrying wire. Current I OUT of page. Right-Hand Rule, 2 Thumb: along I Fingers: curl along B-field lines r = distance from wire r Magnitude of B a distance r from (straight) wire: B

Right Hand Rule 2 wire I Fingers give B!

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.

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

Magnetic Fields of Currents astr.gsu.edu/hbase/magnetic/magfie.html#c1http://hyperphysics.phy- astr.gsu.edu/hbase/magnetic/magfie.html#c1

B Field Inside Solenoids Magnitude of Field anywhere inside of solenoid : B=  0 n I Right-Hand Rule 3 gives Direction: Fingers – curl around solenoid in direction of I Thumb - points in direction B == 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!

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!