The wire shown in the figure (Figure 1)is infinitely long and carries a current I. Figure < 1 of 1 جا 2 Р

Part A Calculate the magnitude of the magnetic field that this current produces at point P. Express your answer in terms of the variables I, a, and appropriate constants. ΟΙ ΑΣΦ . ? B = Submit Request Answer Part B Find the direction of the magnetic field that this current produces at point P. O out of the page into the page Submit Request Answer

## Answer

The magnitude of the magnetic field at point P is given by Biot Savart law.Here only one wire contribute effectively to the magnetic field.The direction of Magnetic field at point p is given by Maxwell's cork screw rule,in this case it is out of the page.

The magnitude of the magnetic field that this euvrent produces at point is can be calculated from Biot - Savant law. According to this law the magnetic field at any point due to a current element i di is given by de = Mo I dix xx 0 where Ř is the vector from the current element to the point of observation and the constant it Mo = An X 107 N/A is called the permeability of free space, P (2,4, 2) À (2,4", 2") 471 R3 I di ( REBR Figgi a current element and p is the point of observation 21 FSX 0001 of 7 00 01 & P OXFSS

The direction of the field dß is perpendiclan to the plane containing the wive and the point p and here it is into the page 11 According to the principle of superposition total field B due to the entire line current I is given by 8 where the integration is over the whole wwvient мо 471 ( I dix arrond wort R3 path. Magnetic field for long straight current carrying wire: 20 B dil Oks Х l O2 XP 13 1 ou ok Fig-2 Let us consider a long - straight wire AB carrying curren I as shown in Fig.-2. Suppose we are to find the magnetic field at any point p at any point a distance from the wire. Let us consider a small element di at a distanie I from o, the foot of the perpendicular from the point p on the wire. According to Biot-Savarh taw the magnetic field at a due to this element is Abd B-Mo I dix alb АЛ R3

Obviously do points towards the plane of the paper This is true for the field produced by all current elements. Hence, total magnetic field at p due to the whole wire would be, gib j olu : Now from fig-2 foldiriladi R sing = die sin (90°+0) IdTXR Mo 45 R3 [:'4=90+0] - dIR cos o or toda esta and la = tano & laa tano so, di= a seco do. Also, & -coso a-coso R R = a seed at a seco.coso a seco do 471 a see o 18)= Mol -019 02 36 Mol ana coso do 01 Mol. (sin Ozt sina) 2 АТИ Site 30 31 where on and on are the values of the angle & corresponding to the end points of the wire. is is = for an infinitely long wire, or Q = 7/2 notaitot har pl = 6 do I 2 - Mol. I bring out mon tromol The direction of B can be easily found by using Manwell's cork screw Bule. According to this aria 2rait sits

if we drive a right-handed cork screw along the direction of current then the direction of rotation of the thumb gives the divection of the magnetic field. tohoto to lo sconti wborn A at the point of observation lies on the extended imaginary portion of the wire, then 01 = 02 = 90° and O, and O2 both are negative. I (singo-singo)=0 (A) 40 a I Now as given in the question wires are infinitely long and carries a current I. Let us name them to understand decarly. Now, as discussed above P point lying on the extended part of AB wire. The magnetic field at point p due to A B wire is o. Now due to BC wire, O2=0, 0 = 90 From egn (2), B = Mo I (or singo) Ата Mol 4Tla

cob The value of magnetic field at point pis MOI 4ria from Manwell. cork serew rule we find that the direction of the magnetic field that this current produces at point is out of the page. bobrotys we no il moitovreado to triod art 010 dl w to writo wie w diodo O Curria-opria) I ON

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