Two parallel, long wires carry currents `i_(1) "and" i_(2)` with `i_(1)gti_(2)`. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 `mu`T. If the direction of `i_(2)` is reversed, the field becomes 30 `mu`T. Find the ratio `i_(1)/i_(2)`.

Options

A. 4
B. 3
C. 2
D. 1

Answer

3

Explanation

Initially when wires carry currents in the same direction as shown. Magnetic field at mid point O due to wires 1 and 2 are respectively
`B_(1)=mu_(0)/4pi .2i_(2)/x ` and `B_(2)=mu_(0)/4pi .2i_(2)/x `
Hence net magnetic field at O , `B_(net)=mu_(0)/4pi .2/x (i_(1)-i_(2))`
`rArr 10 xx10^(-6)= mu_(0)/4pi .2/x (i_(1)-i_(2))` ….(i)
If the direction of `i_(2)` is reversed then
`B_(1)=mu_(0)/4pi .2i_(2)/x `and`B_(2)=mu_(0)/4pi .2i_(2)/x `
So, `B_(net)=mu_(0)/4pi .2/x (i_(1)+i_(2))`
`30xx10^(-6)=mu_(0)/4pi .2/x (i_(1)+i_(2))`
Dividing equation (ii)and (i) `i_(1)+i_(2)/i_(1)-i_(2)rArr i_(1)/i_(2)=2`