A very long wire is held vertical in a direction perpendicular to the horizontal component of Earth's magnetic field. Find the value of current to be passed through this wire so that this resultant magnetic field at a point 10 cm away from this wire becomes zero. What will be the magnetic induction at a point 10 cm away from the wire on the opposite side of this point ?
Horizontal component of Earth's magnetic field `H=0.36xx10^(-4)T,mu_(0)=4pixx10^(-7)Tm//A`.

Explanation

1. `B_(h)=0.36xx10^(-4)T`
`mu_(0)=4pixx10^(-7)(Tm)/A`
`y=10cm=10^(-1)m`
2. As shown in figure, current carrying wire near point O is perpendicular to page.
3. From wire, current comes out of page perpendicular to it.
4. Near point P, magnetic field produced due to current carrying wire and horizontal component of earth magnetic field are in opposite direction, so total (resultant) magnetic field will be zero.
`thereforeB=B_(h)`
`therefore(mu_(0)I)/(2piy)=B_(h)`
`I=(2piyB_(h))/mu_(0)=(0.36xx10^(-4)xx2xxpixx10xx10^(-2))/(4pixx10^(-7))`
`thereforeI=18A`
5. Magnetic field near point `Q=B.=B+B_(h)`
`thereforeB.=2B_(h)`
= `2xx0.36xx10^(-4)`
`thereforeB.=0.72xx10^(-4)T`