THE A MPERE We have learnt that there exists a magnetic field due to a conductor carrying a current which obeys the Biot-Savart law. Further, we have learnt that an external magnetic field will exert a force on a current-carrying conductor. This follows from the Lorentz force formula. Thus, it is logical to expect that two current-carrying conductors placed near each other will exert (magnetic) forces on each other.
In the period - , Ampere studied the nature of this magnetic force and its dependence on the magnitude of the current, on the shape and size of the conductors as well as the distances between the conductors. In this section, we shall take the simple example of two parallel current- carrying conductors, which will perhaps help us to appreciate Ampere’s painstaking work. Figure . shows two long parallel conductors a and b separated by a distance d and carrying (parallel) currents I a and I b , respectively.
The conductor ‘a’ produces, the same magnetic field B a at all points along the conductor ‘b’. The right-hand rule tells us that the direction of this field is downwards (when the conductors are placed horizontally). Its magnitude is given by Eq. [ .
(a)] or from Ampere’s circuital law, a a I B µ The conductor ‘b’ carrying a current I b will experience a sideways force due to the field B a . The direction of this force is towards the conductor ‘a’ (Verify this). We label this force as F ba , the force on a segment L of ‘b’ due to ‘a’. The magnitude of this force is given by Eq.
( . ), FIGURE . Two long straight parallel conductors carrying steady currents I a and I b and separated by a distance d. B a is the magnetic field set up by conductor ‘a’ at conductor ‘b’.