A rectangular loop of wire is placed next to a straight

wire, as shown in Fig. 20–55. There is a current of 3.5 A in
both wires. Determine
the magnitude
and direction of the
net force on the loop

To determine the magnitude and direction of the net force on the rectangular loop, you can use the concept of the magnetic force acting on a current-carrying wire.

The force between two current-carrying wires is given by the formula:

F = (μ₀ / (2π)) * (I₁ * I₂ * L) / d

Where:
F is the magnetic force,
μ₀ is the magnetic constant (also known as the permeability of free space, approximately 4π * 10⁻⁷ T·m/A),
I₁ and I₂ are the currents in the wires,
L is the length of the wire segment where the currents flow parallel to each other,
and d is the distance between the wires.

In this case, we have a current of 3.5 A in both wires, and the wires are placed next to each other. The rectangular loop has a length L and a width d. The forces on the two sides of the loop that are parallel to the straight wire will cancel out each other because they have the same magnitude but opposite directions.

So, the total net force acting on the loop will be determined by the forces acting on the sides of the loop that are perpendicular to the straight wire.

Let's assume the length L of the loop is parallel to the straight wire and the width d is perpendicular to the straight wire. The force acting on the top side of the rectangular loop will be given by:

F_top = (μ₀ / (2π)) * (I₁ * I₂ * L) / d

And the force acting on the bottom side of the rectangular loop will be:

F_bottom = - (μ₀ / (2π)) * (I₁ * I₂ * L) / d (opposite direction)

Since the top and bottom sides are equidistant from the straight wire, the magnitude of the net force on the loop will be:

F_net = |F_top + F_bottom|

Substituting the values, we have:

F_net = (μ₀ / (2π)) * (I₁ * I₂ * L) / d + (μ₀ / (2π)) * (I₁ * I₂ * L) / d

Simplifying, we get:

F_net = (μ₀ * I₁ * I₂ * L) / (π * d)

Now, you can plug in the values for the variables in the formula to calculate the magnitude, and the direction of the force will be determined by the direction of the current in the loop and the straight wire.