The 1200- -turn coil in a dc motor has an area per turn of 1.1 ×10^-2 m^2 The design for the mot

step 1 In this problem, we're given information about a coil, and we want to figure out what the curren

The 1200- -turn coil in a dc motor has an area per turn of...

The $1200-$ -turn coil in a dc motor has an area per turn of $1.1 \times 10^{-2} \mathrm{m}^{2}$ The design for the motor specifies that the magnitude of the maximum torque is 5.8 $\mathrm{N} \cdot \mathrm{m}$ when the coil is placed in a $0.20-\mathrm{T}$ magnetic field What is the current in the coil?

Key Concepts

DC Motor Operation Principles

DC motors operate by converting electrical energy into mechanical energy through the electromagnetic interactions between current-carrying coils and magnetic fields. A thorough understanding of how torque is generated in a coil, via parameters like magnetic dipole moment and the effects of the external magnetic field, is essential for designing motors that meet specific performance criteria, such as a particular maximum torque.

Relationship Between Coil Parameters and Torque

The formula ? = N I A B illustrates how the coil’s characteristics—namely, the number of turns (N), the current (I), and the area per turn (A)—combine with the magnetic field strength (B) to produce a specific amount of torque. This relationship is fundamental in electromechanical systems, as it allows for the adjustment of any of these parameters in order to achieve a desired mechanical performance in devices like motors.

Magnetic Torque on a Current Loop

When a current-carrying loop is placed in a magnetic field, it experiences a torque due to the forces acting on different segments of the loop. This torque tends to rotate the loop and is given by the equation ? = N I A B sin?, where N is the number of turns, I is the current, A is the area of the loop, B is the magnetic field strength, and ? is the angle between the normal to the loop and the magnetic field. Maximum torque is achieved when sin? equals 1, meaning the loop is oriented so that its plane is perpendicular to the magnetic field.

Magnetic Dipole Moment

The magnetic dipole moment of a coil is a measure of its strength in producing a magnetic effect and is defined by the relation ? = N I A. This quantity represents how effectively a current-carrying loop can interact with an external magnetic field, contributing directly to the torque experienced by the loop.

Transcript

Please give Ace some feedback