Two long parallel wires carry currents `i_1 and i_2` such that `i_1 gt i_2`. When the currents are in the same direction, the magnetic field at a point midway between the wires is `6 times 10^-6 T`. IF the direction of `i_2` is reversed, the field becomes `3 times 10^-6 T`. The ratio `i_1/i_2` is

Options

A. `a)1/2`
B. b)2
C. `c)2/3`
D. `d)3/2`

Answer

D

Explanation

When the currents are in the same direction when magnetic field
`B=mu_0/(4 pi) times 2/d [i_1-i_2]`
`6 times 10^-6= mu_0/( 4pi ) times 2/d [i_1-i_2]`……(i)
When the current are in the reversed direction then magnetic field
`B_2=mu_0/(4 pi )times2/d [i_1-(-i_2)]`
or `B_2=mu_0/(4 pi)times 2/d[i_1+i_2]`
or `3 times 10^-5=mu_0/(4 pi ) times 2/d[i_1+i_2]`.....(ii)
Dividing Eq. (i) by Eq. (ii)
`(i_1-i_2)/(i_1+i_2)= (6 times 10^-6)/(3 times 10^-5)`
or `(i_1-i_2)/(i_1+i_2)=2/10`
or `5i_1-5i_2=i_1+i_2`
or `4i_1=6i_2`
or `i_1/i_2=6/4`
or `i_1/i_2=3/2`