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
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 http://hyperphysics.phy- 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!