# A long, vertical wire carrying a current of 10 A in the upward direction is placed in a region where a horizontal magnetic field of magnitude 2.0 × 10–3 T exists from south to north. Find the point where the resultant magnetic field is zero.

Given:
Current in the wire : I = 10 A
Magnitude of Horizontal magnetic field : BO = 2.0 × 10–3 T

For the resultant magnetic field to be zero, we need to have a field in opposite direction to that of the existing field.
Hence, magnetic field B due to wire in the direction from north to south as shown in the diagram..
Formula used:
By Ampere’s Law for a current carrying wire is
Where,

B is the magnitude of magnetic field,

μ0 is the permeability of free space and μ0= 4π × 10-7 T mA-1 d is the distance between the current carrying wire and the required point.
To get zero resultant,
B=BO

d = 0.001 m=1 mm
Hence, the point should be place at a distance of 0.001 m from the wire in west direction

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