Download Magnetic Forces and Torques on Current-Carrying Wires and Loops - Prof. H. Lee and more Study notes Physics in PDF only on Docsity! 28-8. Magnetic Force on a Current-Carrying Wire BvqFB rrr ×= L BLiF rrr ×= 28-8. Magnetic Force on a Current-Carrying Wire 10 g wire of length 20 cm in a B-field 0.5 T. T th t io remove e ens on, (i) what direction is the current? BLiF rrr ×=(ii) what is the magnitude of the current? B force: upward Current: to the right mg = i L B (0.01) (9.8) = i (0.2) (0.5) 28-10. Magnetic Dipole Moment Inner loop: Radius 4 cm, Current 3A, clockwise Outer loop Radius 6 cm, Current 7A, clockwise (i) what is the direction of the net B- AiN rr =μ dipole moment? (ii) what is its magnitude? Currents : both clockwise >> dipole moment: into the page μ = (1) (3) (π 0.042) + (1) (7) (π 0.062) 28-10. Magnetic Dipole Moment AiN rr =μ BU rr ⋅−= μ 28-10. Magnetic Dipole Moment (i) Rank the orientations according to the magnitude of the torque (ii) Rank the orientations according to the potential energy 1 = 2= 3 = 4 1 = 4 > 2= 3 29-2. B-Field Due to a Current 29-2. B-Field Due to a Current 1ˆ0 r̂sdiBd tosdfrom × r v μ 21 4 rsdibyat =v π 0 )(sinidsdB θμ 24 rπ = ∫ ∞ = 2 0 )(sin 4 r dsiB θ π μ ∞− 29-2. B-Field Due to a Current ∫ ∞ = 2 0 )(sindsiB θμ ∞−4 rπ 2/122 i RRθ)( Rsr += 22s n Rsr + == i r B π μ 2 0= 29-2. B-Field Due to a Current B-field at P is zero. Current 2 is (a) into or (b) out of the page? Current 2 is (a) bigger or (b) smaller than the current 1? iB μ0= rπ2 29-2. B-Field Due to a Current B-field at P direction? iμ0 r B π2 = 29-2. B-Field Due to a Current 2 0 )(sin 4 idsdB θμ= rπ 0 )90(sinidsdB μ= 24 rπ φ ϕμ dRi ∫= π 0 2 0 4 R B 29-2. B-Field Due to a Current Semicircle iiB 00 μμ RR 44 π π == Same current (clockwise): Which has the largest magnitude of the B-field at the center ? 29-2. B-Field Due to a Current R1 = 10 cm, R2 = 6 cm Current 0.3 A What is the magnitude of the net B-field at the center ? ii RR B 44 00 μπ π μ == 29-3. Force between Two Parallel Currents iB aμ0= da π2 d iiFBLiF baababybon μ 2 0=⇒×= vvr π 29-4. Ampere‘s Law enclosedisdB 0μ=•∫ rr Line integral of B-field Andre-Marie Ampere (1775–1836) 29-4. Ampere‘s Law l disdB 0μ=•∫ rr enc ose Sign of the current? 29-4. Ampere‘s Law Same current (parallel or antiparallel): Rank the loops according to the magnitude of the integral ∫ • sdB rr enclosedisdB 0μ∫ =• rr 29-4. Ampere‘s Law A Long Line of Current (Inside) )2( rBdsBsdB π==• ∫∫ rr ⎟⎟ ⎞ ⎜⎜ ⎛ = 2rii π ⎠⎝ 2Renc π r R iB 2 0 2 μ = π 29-5. Solenoids l dSo enoi 29-5. Solenoids Ideal Solenoid • No B‐Field outside U if I id• n orm ns e )( hniNiienc == :n # of turns per unit length 000 +++=•∫ hBsdB rr )( inB μ= 0
