A long straight vertical wire carries a current of 10 A flowing upwards through it at a place where the horizontal component of the earth's magnetic induction is 0.3 gauss. Then the total magnetic induction at a point 5 cm from the wire due magnetic north of the wire is

detailed solution

Correct option is B

The magnetic induction B due to a current I ampere in a long straight conductor at a distance r metre from it is given byB=μ04π × 2IrHere  I=10  A,  r=5  cm  =  5  ×  10−2 mB=10−7 ×  2 × 105 × 10−2 = 0.4  gaussSince the point is due to magnetic north of the conductor, the line of action of B→ is along east-west direction. Magnetic induction due to earth's horizontal component is 0.3 gauss in a direction from south to north.Resultant magnetic induction Br is given by Br = 0.42 + 0.32  = 0.5  gauss