Two long straight wires carrying the same current I and separated by a distance r exert a force F on each other.If the current is increased to 4I...

According to Ampere's law, the force between two wires
carrying a current I1 and I2 and which are separated by a distance r is given as F=
2*K*I1*I2 / r, where K is a constant.

In the problem, when
the wires carried a current I and were separated by a distance r the force was
F

=> Fo = 2*K*I^2 /
r

Now when the current is increased to 4I and the
separation reduced to r/6, the new force is given by:

Fn =
2*K*(4I)^2 / (r/6)

=>
2*K*16*I^2*6/r

=>
2*K*I^2*(16*6)/r

=>
Fo*(16*6)

=>
Fo*(96)

Therefore the new force between the
wires is 96 times the original force.