Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other

The value is  

Explanation:

From the question we are told that  

     The current on first  wire is

     The current on the second wire is

     The distance of separation is

     The distance from the first wire considered is a =  20 cm  =  0.2 m

      The distance from the first wire considered is b = 60 cm  =  0.60 m

Generally the magnetic field in the plane of the wires is mathematically represented as

The reason for the positive sign is because the current are moving in opposite sides

Here  

and

So

=>  

Here is the permeability of free space with value

So

=>  

=>