Question

A square loop 10cm on a side carries a current I' = 1A, and is placed 10cm away from a long,straight wire of current I = 10A, which is in the plane of the loop. Calculate the net force on the loop (in Newtons). Is the loop attracted to or repelled from the straight wire?

Answer 1

i1 =10A, i2 =1A sde a=10cm=0.1 m, distance between the straight cureent and the side 12 of the loop is b=10 cm =0.1 m

Assume that the directions of the currents are following :
i1↑I ⃞ ↓i2
Points 1,2,3, and 4 are located clockwise starting from the left bottom corner of the square

Magnetic field of the current i1
at the side 12 locations is
B12 =μ₀•i1/2•π•b =4π•10⁻⁷•10/2•π•0.1 = ..
Magnetic field of the current i1 at the side 34 location is
B34 =μ₀•i1/2•π•(a+b) = 4π•10⁻⁷•10/2•π•0.2 = ..
Ampere’s force on the side 12 is
F12=i2•a•B12 =
=1•0.1• 4π•10⁻⁷•10/2•π•0.1=...
Ampere’s force on the side 34 is
F12=i2•a•B34 =
=1•0.1• 4π•10⁻⁷•10/2•π•0.2=...

F23=F41. These forces are directed in opposite directions, =>

The net force is directed to the left (to the straight current) and is
F= F12 –F34 =….