A long, straight wire carries a current i. Let B 1 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 B 2 be the magnetic field at this point due to this section only. Find the value of d/ℓ so that B 2 differs from B 1 by 1%.

Question

Philoid · Accepted Answer

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,

⇒