Question

A straight wire that is infinitely large has a current I, and is partially surrounded by a closed spiral of current that is formed by two semicircular sections and two straight sections (as shown on the image below). The spiral has a length L, radius R and has a current 12, The axis of the spiral coincides with the one from the wire. Calculate the force on the loop. R L Hol211L î Answer: TER

Answer 1

A C L 19 E I, ↑ Magnetic field field at a distance from current earrying an infinitely long wire} = B = Mo. I, A 2 TV CSscanned with CamScanner

ore we 12 for section ABC Bri 1,1 and magnetic from the figure see that the angle between current field is always 180° :. Magnetic force per unit length of section IgxBg = Iz B, Sin(180°) the ABC a 0 similarly, force per th of the loc force per unit Loop Section DEF co (Here, the angle between a and I Iq is unit lengi is 0') CScanned with CamScanner

for the portions AF and CD → we can for CD length consider, И Т. RAR. C Bi 6) [ie magnetic field is pointing into the Page for the section of F I : Force per unit length of el A = ?zx Bi =(13) CÔ xk) Mo It fz M ZAR me Is Iz ZAR RTR similarly Mol. 2TR force for AF portion, i per unit length of Af 욘 = In * B (I2 }) x ( 1 Moll RAR do I, fe ha RAR ws CS$canned with CamScanner

... Total force on the loop E = fith - 2x do I 1 Izmir LAR F = Mo I, IL (Proved) a TR for a current carrying wire → R X IT CScanned with CamScanner