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?
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 =….
To calculate the net force on the square loop, we need to determine the forces acting on each side of the loop and find the vector sum.
The force between a current-carrying wire and a loop can be determined using Ampere's Law, given by:
F = (µ₀ * I₁ * I₂ * L) / (2 * π * r)
Where:
F is the force between the two currents,
µ₀ is the permeability of free space (4π x 10^-7 Tm/A),
I₁ and I₂ are the currents in the wires,
L is the length of the wire in question,
r is the distance between the wire and the loop.
In this case, the loop and the wire are parallel, so the force acting on each side of the loop will be the same. The force acting on each side of the loop can be calculated as follows:
F₁ = (µ₀ * I' * I * l) / (2 * π * r₁)
Where:
F₁ is the force on the loop due to the current in the wire,
I' is the current in the loop,
I is the current in the wire,
l is the length of the side of the loop,
r₁ is the distance between the wire and the loop.
Since the loop is square and each side is 10 cm, the length of each side (l) would be 0.1 m.
Given that I' = 1 A, I = 10 A, and r₁ = 10 cm = 0.1 m, we can calculate the force on each side of the loop:
F₁ = (4π x 10^-7 Tm/A * 1 A * 10 A * 0.1 m) / (2π * 0.1 m)
= (4π x 10^-7 Tm/A * 1 A * 10 A * 0.1 m) / (2π * 0.1 m)
= (4π x 10^-6 N) / (2π)
= 2 x 10^-6 N
Since the force on each side of the loop is the same, the net force on the loop can be calculated by multiplying the force on one side by the number of sides in the loop, which is 4:
Net force = 4 * F₁
= 4 * (2 x 10^-6 N)
= 8 x 10^-6 N
Therefore, the net force on the loop is 8 x 10^-6 N.
To determine whether the loop is attracted to or repelled from the straight wire, we need to consider the direction of the forces. Since the loop and the wire are parallel, the forces on each side of the loop will be in the same direction. Since the net force on the loop is positive (in the outward direction), the loop will be repelled from the straight wire.
Therefore, the loop is repelled from the straight wire.