Question
Write the formula for the force per unit length between two parallel current carrying wires. Using it, write the definition of Ampere and Coulomb.
✓
Answer
→As shown in the figure, two long wires $a$ and $b$ are placed parallel. The (perpendicular) distance between them is $d$. The current passing through them are $I _a$ and $I _b$ respectively.
→The force exerted by wire $a$ on a segment of length L on wire $b$ is
$F _{b a}=\frac{\mu_0 I _a I _b L}{2 \pi d}$
→Force per unit length
$f_{b a}=\frac{ F _{b a}}{L}=\frac{\mu_0 I _a I _b}{2 \pi d}$
→Similarly,
$f_{a b}=\frac{ F _{a b}}{L}=\frac{\mu_0 I _a I _b}{2 \pi d}$
→If we take $I _a= I _b=1 A$ and $d=1 m$ in above equation then
$f_{a b}=f_{b a}=2 \times 10^{-7} N$
→Definition of 1 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 $2 \times 10^{-7}$ Newtons per metre of length."
→1 Coulomb : "When a steady current of 1 A is set up in a conductor, the amount of charge passing through its cross-section in 1 s is 1 coulomb."
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