Question

Two straight parallel wires, both carrying 10 amperes in the same direction attract each other with a force of 1 x 10-3 N. If both currents are doubled, then force of attraction will be :

• A. 1 x 10-3 N
• B. 2 x 10-3 N
• C. 4 x 10-3 N
• D. 0.25 x 10-3 N

Answer 1

The correct option is C 4 x 10-3 N

Answer is C.
If two parallel wires have currents traveling in the same direction, the magnetic fields generated by those currents between the wires will both point in opposite directions resulting in the wires attracting each other.
The formula used to calculate these attractive or repulsive forces is: $F=B_{perpendicular}IL$.That is, $F_{12}=\left(o{I}_1/2r\right)I_2{L}_2$
$F_{12}=\left(o/2r\right)I_1{I}_2{L}_2$
Thus, $F_{12}=(2\times {10}^{-7}/r)I_1{I}_2{L}_2$.
Hence, if the current is doubled in the parallel wires, the attractive force increases by 4 times. That is, $4\times {10}^{-3}N$.