Question

Two wires carrying equal current $I$ are a distance $a$ apart.
If the current through wire one is doubled while the current through the wire two is tripled, what is the ratio of the force that wire two exerts on wire 1 ($F_1$) to the force that wire one exerts on wire 2 ($F_2$)?

• A. 4:09
• B. 2:03
• C. 1:01
• D. 3:02
• E. 9:04

Answer 1

The correct option is C 1:01

The force between two long parallel current ($I_1,I_2$) carrying wire separated by a distance $a$ is given by ,

$F=\frac{{\mu }_0{I}_1{I}_{2}L}{2\pi a}$ ,

this is the force exerted by wire 2 on wire 1 and by wire 1 on wire 2 , which depends on the product of current in both wire , therefore change in currents in the wire will affect the force between them but they will exert equal force on each other i.e. $F_1/F_2=1/1$ , or $F_1:F_2=1:01$