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Find vecB at the origin due to the long ...

Find `vecB` at the origin due to the long wire carrying current I.

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Net magnetic field at origin is the vector sum of magnetic fields
due to wires (1) ,(2),(3), and (4).
`vecB=vecB_1+vecB_2+vecB_3+vecB_4`
where `B_1=0`, as direction of current wire passes through origin.
Magnetic field due to wire (2),
`vecB_2=(mu_0)/(4pi) I/A[sin 0^@+sin45^@] hatj`
Magnetic field due to wire (2) and wire (3) is equal to `vecB_2=vecB_3`
`implies vecB_2=vecB_3=(mu_0I)/(4sqrt2pia)hatj`
Magnetic field due to wire (4),
`vecB_4=(mu_0)/(4pi) I/a[sin 0^@+sin90^@] hatk=(mu_0I)/(4pia)hatk`
So, `vecB=2vecB_2+vecB_4=(mu_0I)/(4pia)[sqrt2hatj+hatk]`
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