Two parallel, long wires carry currents i1 and i2 with i1> i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 μT. If the direction of i2 is reversed, the field becomes 30 μT. The ratio i1/i2 is
The magnetic field caused by a long wire is given by where i is the current in the wire, d is the distance at which B is to be calculated, μ0 is the magnetic permeability of free space. Let the distance between the two wires be 2d.
Then, when the currents are parallel, one’s magnetic field will negate the other’s because at the point midway between the two wires, the magnetic fields generated by them will be directed in the opposite directions and it can be verified by the right hand Cork-Screw rule.
So the total B will be
which is given to be 10μT and when the direction of i2 is reversed then, is given to be 30μT. So, solving these, we get,
(Componendo- Dividendo rule)
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