Question

There are two parallel current carrying wires X and Y as shown in figure. Find the distance of a point from wire X, where the resultant magnetic field is zero.

Answer 1

Here, `I_1=10A, I_2=20A`.
`r=10cm=0.10m`.
Let P be a point in a space between two wires, at a perpendicular distance x from wire X, where resultant magnetic field is zero. Then
magnetic field at P due to current in wire X = magnetic field at P due to current in wire Y
`(mu_0)/(4pi)(2I_1)/(x)=(mu_0)/(4pi)(2I_2)/((r-x))` or `I_1/x=(I_2)/((r-x))`
or `10/x=(20)/(0.10-x)` or `2x=0.10-x`
or `3x=0.10` or `x=0.10/3` or `x=0.033m`