A long, straight wire carries a current i. Let B1 be the magnetic field at a point P at a distance d from the wire. Consider a section of length ℓ of this wire such that the point P lies on the perpendicular bisector of the section. Let B2 be the magnetic field at this point due to this section only. Find the value of d/ℓ so that B2 differs from B1 by 1%.
Magnitude of current = i
Distance of point P from wire = d
The magnetic field induced in the wire is defined as
Also, the magnetic field due to a section of length l on the perpendicular bisector is given by
Neglecting (as it is very small), we get
now,
We are given that,
⇒
substituted the value of in the above equation we get,
⇒
⇒
⇒