The distance between two long straight conductors is 5m. Currents `2.5A` and 5A are flowing through them in the same direction. What will be the magnetic field at the mid-point betwen them ?

Explanation

According to the corkscrew rule, the magnetic fields at the mid-point due to the conductors will be opposite in direction.
So, the relation `B=(mu_(0))/(4pi)*(2l)/(r)`, gives,
magnetic field at the mid-point due to the second conductor,
`B_(1)=(mu_(0))/(4pi)*(2I_(1))/((r)/(2))=(mu_(0))/(4pi)*(4I_(1))/(r)`
and magnetic field at the mid-point due to the second conductor,
`B_(2)=(mu_(0))/(4pi)*(2I_(2))/((r)/(2))=(mu_(0))/(4pi)*(4I_(2))/(r)`
`I_(2) gt I_(1)` and hence `B_(2) gt B_(1)`
`:.` The resultant magnetic field,
`B=B_(2)-B_(1)=(,u_(0))/(4pi)*(4)/(r)(I_(2)-I_(1))`
`=(mu_(0))/(4pi)*(4)/(5)(5-2.5) =(4pixx10^(-7))/(4pi)xx(4)/(5)xx 2.5`
`[ :. r=5, I_(1)=2.5a, I_(2)=5A]`
`=2xx10^(-7)T`