Question

10. The figure shows six sets of five equally spaced, long parallel wires carrying electric currents of equal magnitudes into or out of the page. Rank the magnitude of the magnetic forces acting on the central wire in each scenario, due to the currents in the other four wires, from greatest to smallest. Support your ranking with the appropriate calculations/justifications. O O O A O O O o B O O С O ♡ ♡ O D E O ♡ o F O O

Answer 1

Question 10 29 ta-44-59-19 O O A o O O @ C o D ♡ a o E Given : All the wires are equally spaced, long parallel wises cas yung equal electis sevente Juid Magnetise force at central avise. In set A hit the distance between each wire is 'al and magnitude of current flowing through each wire be force due to wires force on curent carrying wie placed in ingegnetic field F = SI dl X Bi 2 3 y 5 ow LO -20 24

sue to 2017 Here, magnetic field is present due to 4 wires - long wire Magnetic field = Mo I can Xô) J Ilal, 7) X Bi + f I (dlg 1) x B 2 + SI( de ) x B x + JI (dl= (1) X BS Due to Wue I wine 2 force on Central wire wire 3 wire 4. and of M.E. Direction of magnetic field can also be found by pointing thumb in ir current finger curling direction is the direction I (2a) lo I (îXC-)) + Ila) Lot (1x). 27 (2a) 27(a) (-1X (f)) + I (24) les I (-1X -7) 27 (a) 21(2a) dup I ² tk) + dis 12 k + ho I 2 K + Mo I2 k + I (a) do I 21 25 27 = 2410 I² k 2 T = Mo 1² T

Similarly, We will proceed for other cases. Set B 3 4 а. a TE- / I (2aî)x bis I (1) + 20(20) I can Xho I (g) 2a(a) + I (al-1))Xl0I () + I (2014) do I (4) 2A(2) ana cats Mo I 2 2T + Mo I² k t ho I2 Ř tho I k 21 27 27 f3 240 I 2 for set (8) Set ca 2 4 LO

ho I (2a) î x do I ) + Ica?) X Mo I (-) 2καν 2x(24) + I (a) (-1) X do I (-J) + I (20)(-7) 46 I 1-7) Mo I² k & lo I² (-k) + tho 12 (2) + hol? (K) 2a zna ata 20 25 24 16 lo I 2 (R) (case 3) ㅈ For set c. - det D. 2 3 X + fz = I (2a)? l I l-f) + 'I can hur I (-1) 2na 20 (20) & I (a) (-1) Mo IX (-9) + I(29) (-2) X dhe I (J) 27(a) 27 (2a) = lo7? [-R-X +x=8] – La I" (*) 20

2A 29 O y 2 3 Ah 수 I = I (29) Î x duo I l-f) + Ilai) X o I (J) 2 (20) Ilac-?)) do I -9) + I (201-2))xlust (9) + 2ra 2na I² [ - R + h + k k 21 F = 0 Set f : la lon 2 3 4. -1 ana I(2a) 1 X do I (-)) & Ia (?) x Mo I (-2) 20(23) 7. I lol-?)) lueg) + DOC-1) din 21 (20) ata

E = 10 12 [ - K - R tk tk 27 1 = 0 Е, 20 I² ñ (k) So I2 T C k) Set I (A) set 2 (6) set 3 (c) set 4 CD) Set 5 (E) Set 6 (f). ho 12/25 (-k) 10 Set B y Set A = Set C 7 Set D Y Set E= Set of