Moving Charges and Magnetism — Physics STD 12 Science — Question

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

$\text{B}_{\alpha} = \frac{\mu_\circ\text{I}_{\alpha}}{2\pi\text{d}}$

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’. 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

$\int_{ba} = \text{I}_{b}\text{LB}_{a}$ $ = \frac{\mu_\circ\text{I}_{a}\text{I}_{b}}{2\pi\text{d}}\text{L}$

Let $\int_{ba}$ represent the magnitude of the force $\text{F}_{ba}$ per unit length.

$\int_{ba} = \frac{\mu_\circ\text{I}_{a}\text{I}_{b}}{2\pi\text{d}}$

One ampere: The ampere is the value of that steady current which, when maintained in each of the two very long, straight, parallel conductors of negligible cross-section, and placed one metre apart in vacuum, would produce on each of these conductors a force equal to 2 × 10^–7 newton per metre of  their length.