Question

Definition of Ampere —

Answer 1

Definition of Ampere —

Let $I_1=I_2=1 \mathrm{~A}, r=1 \mathrm{~m}$

then $\frac{F}{l}=\frac{4 \pi \times 10^{-7} \times 1 \times 1}{2 \pi \times 1}=2 \times 10^{-7} \mathrm{~N} \mathrm{~m}^{-1}$

Thus, the ampere is that constant current which when maintained in two straight parallel conductors of infinite length and of negligible circular cross section placed one metre apart in a vacuum would produce a force between the conductors equal to $2 \times 10^{-7}$ newton per metre.

If two linear current carrying conductors of unequal length are held parallel to each other, then the force on a long conductor is due to magnetic field interaction due to currents of short conductor and long conductor.

If $l, L$ be lengths of short and long conductors and $I_1, I_2$ be currents through shori and long conductors respectively and $r$ is the separation between these two parallel conductors, then the force on long conductor $=$ force on short conductor $=\frac{\mu_0}{4 \pi} \frac{2 I_1 I_2}{r} l$.

When two charges $q_1$ and $q_2$ respectively moving with velocities $v_1$ and $v_2$ are at a distance $r$ apart, then the force acting between them is

$F=\frac{\mu_0}{4 \pi} \frac{q_1 q_2 v_1 v_2}{r^2}$

• If $q_1$ and $q_2$ are of the same nature and they move in the same direction, then the force acting between them is attractive.
• If $q_1$ and $q_2$ are of the same nature and they move in the opposite directions, then the force acting between them is repulsive.