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# a long wire with current I is bifurcated as shown in the figure dividing curent equally.The magnetic feild at point (0,a) is :

Let us assume the wire along the +y-axis direction in which cureent (i/2) is passing is semi infinite with
respect to test point P(0,a), i.e, length of wire is upto +∞

Similarly , we assume, the wire along the -y-axis direction in which cureent (i/2) is passing is semi infinite with
respect to test point P(0,a), i.e, length of wire is upto -∞

we determine the magnetic induction due to current (i/2) passing along +y-axis direction and -ve y-axis direction separately

Figure given below shows the procedure of getting magnetic induction due to current (i/2) in +y-axis direction
Let us consider small current element (i/2)dy at Q(-a,y) .

Magnetic induction dB at  P(0,a) due to this small current element is given by ,

dB = [ (μo i ) / 8π ] { dy / [ (y-a)2 + a2 ] }   ......................(1)

Magnetic induction B due to full length of wire

..............................(2)

Similarly we calculate magnetic induction B due to current (i/2) passing in -y-direction as shown below
dB = [ (μo i ) / 8π ] { dy / [ (y+a)2 + a2 ] }   ......................(2)

................(3)
from eqn.(2) and (3), we see that both magnetic induction vectors are equal in magnitude but in opposite in direction.

Hence net magnetic induction at point P(0,a) is zero

Answered by Expert 6th January 2020, 8:46 AM
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