The magnetic field at a point midway between two parallel long wires carrying currents in the same direction is `10 mu T`. If the direction of the smaller current among them is reversed, the field becomes `30 mu`T. The ratio of the larger to the smaller current in them is

Options

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

Answer

B

Explanation

Let `I_1 gt I_2`
Then, `(mu_0)/( 2pi r) (I_1 - I_2) = 10 mu T" "...(i)`
and `(mu_0)/( 2pi r ) (I_1 + I_2) = 30 mu T" "...(ii)`
Now, divide Eq. (i) by Eq. (ii), we get
`(I_1 - I_2)/(I_1 + I_2) = (10)/(30)`
`(I_1 - I_2)/( I_1 + I_2) = (1)/(3)`
`3 I_1 - 3I_2 = I_1 + I_2`
`3I_1 - I_1 - 3I_1 - I_2 =0`
`2I_1 = 4I_2`
`(I_1)/(I_2) = (4)/(2) = (2)/(1)`
Hence, the ratio of `I_1 : I_2 = 2:1`