Question 230 of 276

Two long straight parallel wires, carrying (adjustable) currents ${I}_{1}$ and ${I}_{2}$ , are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $F$, on the product ${I}_{1}{I}_{2}$ , would be:

ABCD

Show answer and solution▾

Answer: (D)

Force between two parallel current carrying wires is given as

$f=\dfrac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi d}l$

$F\propto {I}_{1}{I}_{2}$

When ${I}_{1},{I}_{2}$ are in same direction the ${I}_{1}{I}_{2}is+ve$ ⇒ attraction ⇒ -ve

When ${I}_{1}{I}_{2}$ are in opposite direction then

${I}_{1}{I}_{2}=-ve$

$∴$ Force = repulsive = +ve