Question

Two current carrying wires are a distance $a$ apart and experience a Force $F$ between them. The wires are moved a distance 2$a$ apart.
Which of the following is a possible value for the new force between the wires?

• A. $\frac{1}{4}F$
• B. $\frac{1}{2}F$
• C. $F$
• D. $2F$
• E. $4F$

Answer 1

The correct option is B $\frac{1}{2}F$

Force between two parallel current carrying wires $F=\frac{{\mu }_o}{2\pi }\frac{I_1{I}_2}{a}$

New distance between the wires $a^{\prime }=2a$

$\therefore$ New force $F^{\prime }=\frac{{\mu }_o}{2\pi }\frac{I_1{I}_2}{2a}=\frac{F}{2}$