Two parallel, long wires carry currents `I_(1) and I_(2)` with `I_(1) >I_(2)` When the current are in the same direction , the magnetic field at a point minway between the wires is the `10mu`T, if the direction of `I_(2)` is reversed , the field becomes`30mu` T. find the value of `I_(1)/I_(2)`.

Explanation

Case I
At P,`B_(I)=(mu_(0)I_(1))/(2pid)-(mu_(0)I _(2))/(2pid)`
`B_(I)=(mu_(0)(I_(1)-I_(2)))/(2pid)=10muT`
CaseII
At P,`B_(2)=(mu_(0)I_(1))/(2pid)-(mu_(0)I _(2))/(2pid)`
`=(mu_(0))/(2pid)(I_(1)-I_(2))=30muT`
`:.(B_(1))/(B_(2))=(I_(1)-I_(2))/(I_(1)+I_(2))=(10muT)/(30muT)`
`=(I_(1)-I_(2))/(I_(1)+I_(2))=(1)/(3)`
Using componenedo and dividendo rule,
`((I_(1)-I_(2))+(I_(1)+I_(2)))/((I_(1)-I_(2))-(I_(1)+I_(2)))=(1+3)/(1-3)implies (I_(1))/(-I_(2)) =2`