A long vertical wire in which a current is flowing produces a neutral point with the earth's magnetic field at a distance of 5 cm from the wire. If the horizontal component of the earth's magnetic induction is 0.18 gauss, then the current in the wire is

The magnetic induction B due to current I ampere in a long straight conductor at a distance r metre from it is given byB=μ04π ×  2IrHere,  r=5  cm = 5  ×  10−2 m∴    B=10−7 ×  2 × I5 × 10−2=  0 .04 I  Gauss At the neutral point, the magnetic induction due to earth's horizontal component is equal and opposite to that due to current in the conductor.∴     4I  ×  10−2 =  0.18  or  I  =  4.5  A