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1. Intro to Physics Units1h 29m
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32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

28. Magnetic Fields and Forces

Force and Torque on Current Loops

Physics

28. Magnetic Fields and Forces

Force and Torque on Current Loops

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4:00 minutes

Problem 39b

Textbook Question

What is the loop's equilibrium orientation?

Verified step by step guidance

Understand the context of the problem: The equilibrium orientation of a loop typically refers to the position where the net torque acting on the loop is zero. This often involves analyzing the interaction between the magnetic field and the current-carrying loop.

Identify the forces and torques acting on the loop: A current-carrying loop in a magnetic field experiences a torque due to the interaction between the magnetic moment of the loop and the magnetic field. The torque is given by the vector equation:

τ = μ × B

, where

μ

is the magnetic moment of the loop and

B

is the magnetic field.

Determine the magnetic moment of the loop: The magnetic moment

μ

is calculated as

μ = I A

, where

I

is the current in the loop and

A

is the area vector of the loop. The direction of

A

is determined by the right-hand rule.

Set the condition for equilibrium: For the loop to be in equilibrium, the torque must be zero. This happens when the magnetic moment

μ

is aligned with the magnetic field

B

. Mathematically, this means the angle

θ

between

μ

and

B

is zero (parallel) or 180 degrees (antiparallel).

Conclude the equilibrium orientation: The loop's equilibrium orientation is when its plane is perpendicular to the magnetic field, and the magnetic moment vector is either aligned (parallel) or anti-aligned (antiparallel) with the magnetic field direction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium

Equilibrium in physics refers to a state where all forces and torques acting on an object are balanced, resulting in no net force or rotation. In the context of a loop, this means that the gravitational force, tension, and any other forces are in balance, allowing the loop to maintain a stable position without accelerating or rotating.

Torque

Torque is a measure of the rotational force applied to an object, which causes it to rotate around an axis. The equilibrium orientation of a loop is influenced by the torques generated by various forces acting on it, such as gravity and tension. For the loop to be in equilibrium, the sum of the torques must equal zero.

Center of Mass

The center of mass is the point in an object where its mass is evenly distributed in all directions. For a loop, the center of mass plays a crucial role in determining its equilibrium orientation, as the loop will tend to orient itself such that the center of mass is at the lowest possible point, minimizing potential energy and achieving stability.

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Related Practice

Textbook Question

(I) If the current to an electric motor drops by 18%, by what factor does the output torque change?

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Textbook Question

How much work is required to rotate the current loop (Fig. 27–23) in a uniform magnetic field $\vec{B}$ from (a) θ = 0° ( $\vec{μ}$ ∣∣ $\vec{B}$ ) to θ = 180°, (b) θ = 90° to θ = -90°.

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Multiple Choice

A square loop of wire has a side length of

12 cm

and carries a

10 A

current. What is the size of its magnetic dipole moment?

A single circular loop of wire has a radius of

2 . 0 cm

, and carries a current of

4.0 A

. What is the maximum torque that could be experienced by this loop due to earth's magnetic field?

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views

Textbook Question

A small bar magnet experiences a 0.020 N m torque when the axis of the magnet is at 45° to a 0.10 T magnetic field. What is the magnitude of its magnetic dipole moment?

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Textbook Question

What is the magnitude of the torque on the current loop in FIGURE EX29.39?

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Textbook Question

A rectangular loop of wire carries a 2.0-A dc current and lies in a plane which also contains a very long straight wire carrying a 10.0-A current as shown in Fig. 28–58. Determine (a) the net force and (b) the net torque on the loop due to the straight wire.

457

views

Textbook Question

(II) An iron atom has a magnetic dipole moment of about 1.8 x 10^-23 A m². (a) Determine the dipole moment of an iron bar 15 cm long, 1.2 cm wide, and 1.0 cm thick, if it is 100 percent saturated. (b) What torque would be exerted on this bar when placed in a 0.80-T field acting at right angles to the bar?

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