Q16 of 92 Page 249

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,


⇒


⇒


⇒


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