A 20.0 cm ×30.0 cm rectangular loop of wire carries 1.0 A of current clockwise around the loop.

step 1 All right, this time we have a loop of wire, rectangular, 20 centimeters by 30 centimeters with

A 20.0 cm ×30.0 cm rectangular loop of wire carries 1.0 A of...

A $20.0 \mathrm{cm} \times 30.0 \mathrm{cm}$ rectangular loop of wire carries $1.0 \mathrm{A}$ of current clockwise around the loop. (a) Find the magnetic force on each side of the loop if the magnetic ficld is 2.5 T out of the page. (b) What is the net magnetic force on the loop?

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Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept involves understanding that a current-carrying conductor in a magnetic field experiences a force described by F = I (L x B), where I is the current, L is the vector representing the length and direction of the current, and B is the magnetic field. The magnitude of the force depends on the current, the length of the conductor within the field, and the sine of the angle between the current direction and the magnetic field, while the direction is determined by the right-hand rule.

Force Cancellation in Closed Current Loops

When a closed loop of wire is placed in a uniform magnetic field, each segment of the loop experiences a force; however, because the loop is closed, forces on opposite sides—if they are equal in magnitude and opposite in direction—cancel each other out, resulting in a zero net force on the loop. This principle is essential for understanding the overall behavior of current loops in magnetic fields and is particularly useful in analyzing systems where the loop shape and field uniformity simplify the vector summation of forces.

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