posted by Rachel .
Two very long, straight, parallel wires carry currents that are directed perpendicular. Wire 1 carries a current I1 into the page (in the -z direction) and passes through the x axis at x = +a. Wire 2 passes through the x axis at x = -2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2µ0I1 / ( 2πa ). The current I2 can have either of two possible values.
Find the value of I2 with the smaller magnitude, stating it in terms of I1 and giving its direction.
I have to write formula
Not exactly write a formula. You have to analyze the problem, then derive the formula. We don't write formulas in Physics, the Creator did that.
Here first find the distance between wires (so what is the distance between x=-2a and x=a) The force at the origin? Well it is the sum of the two forces from each wire.
Force from wire1 is kI/(2pi*distance)
The other force is similar, but the distances are different.
Now signs. Use your right hand rule, and determine the force direction for each wire. You don't know the direction for current I2, but if it is into the page, then the force subtracts from the first force.
Well, add the forces, with the +- force for the second force.