A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.40 A , is oriente

step 1 A given problem we have a following situation. A coil is inside a loop I should say. A loop is i

A rectangular coil of wire, 22.0 cm by 35.0 cm and...

A rectangular coil of wire, 22.0$\mathrm { cm }$ by 35.0$\mathrm { cm }$ and carrying a current of $1.40 \mathrm { A } ,$ is oriented with the plane of its loop perpendicular to a uniform $1.50 - \mathrm { T }$ magnetic field, as shown in Fig. E27. 46. (a) Calculate the net force and torque that the magnetic field exerts on the coil. (b) The coil is rotated through a $30.0 ^ { \circ }$ angle about the axis shown, with the left side coming out of the plane of the figure and the right side going into the plane. Calculate the net force and torque that the magnetic field now exerts on the coil. (Hint: In order to help visualize this three-dimensional problem, make a careful drawing of the coil as viewed along the rotation axis.)

A rectangular coil of wire, 22.0$\mathrm { cm }$ by 35.0$\mathrm { cm }$ and
carrying a current of $1.40 \mathrm { A } ,$ is
oriented with the plane of its
loop perpendicular to a uniform
$1.50 - \mathrm { T }$ magnetic field, as shown
in Fig. E27. 46. (a) Calculate the
net force and torque that the
magnetic field exerts on the coil. (b) The coil is rotated through a $30.0 ^ { \circ }$ angle about the axis shown,
with the left side coming out of the plane of the figure and the right
side going into the plane. Calculate the net force and torque that the magnetic field now exerts on the coil. (Hint: In order to help
visualize this three-dimensional problem, make a careful drawing
of the coil as viewed along the rotation axis.)

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a moving charge in the presence of electric and magnetic fields. In the context of current-carrying conductors, this force is calculated as F = I (L x B), where I is the current, L is the length vector of the conductor, and B is the magnetic field. This principle describes how segments of a conductor within a magnetic field experience a force perpendicular to both the current direction and the field, and is foundational in understanding the behavior of electromagnetic devices.

Magnetic Torque

Magnetic torque arises when a current-carrying loop is placed in a magnetic field. The torque, given by the cross product ? = ? x B, depends on the magnetic dipole moment of the loop and the magnetic field. This torque tends to rotate the loop so that its magnetic dipole moment aligns with the magnetic field. The concept is crucial for understanding how electric motors and galvanometers function, where rotational motion is generated by electromagnetic interaction.

Magnetic Dipole Moment

The magnetic dipole moment, typically denoted as ?, quantifies the strength and orientation of a current loop’s magnetic properties. It is defined as ? = I·A, where I is the current and A is the area vector of the loop. This concept is essential when analyzing the rotational effects (torque) on current loops in magnetic fields, as it directly relates the geometrical and electrical properties of the loop to its magnetic behavior.

Uniform Magnetic Field

A uniform magnetic field is one in which the magnetic field lines are parallel and evenly spaced, leading to a constant magnitude and direction throughout a region. In problems involving current loops, this uniformity means that while individual segments may experience forces, the net translational force on a closed loop in such a field often sums to zero. However, non-zero net torque can still be produced, making the analysis of these systems both elegant and important for understanding electromagnetic interactions.

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