An electric dipole consists of two opposite charges ±q±q separated by a small distance ss. The product p=qsp=qs is called the dipole moment. Figure P22.6122.61 shows an electric dipole perpendicular to an electric field EE. Find an expression in terms of pp and EE for the magnitude of the torque that the electric field exerts on the dipole.

Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

All textbooks

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problem 61

Chapter 22, Problem 61

An electric dipole consists of two opposite charges $\pm q$ separated by a small distance $s$ . The product $p = q s$ is called the dipole moment. Figure P $22.61$ shows an electric dipole perpendicular to an electric field $E$ . Find an expression in terms of $p$ and $E$ for the magnitude of the torque that the electric field exerts on the dipole.

Verified step by step guidance

Understand the concept of torque on a dipole: Torque (τ) is the rotational effect of a force. For an electric dipole in an electric field, the torque depends on the dipole moment (p), the electric field (E), and the angle (θ) between them.

Recall the formula for torque on a dipole: The magnitude of the torque is given by τ = pE sin(θ), where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment vector and the electric field vector.

Identify the given situation: The problem states that the dipole is perpendicular to the electric field. This means the angle θ between the dipole moment and the electric field is 90 degrees.

Substitute θ = 90° into the torque formula: Since sin(90°) = 1, the torque simplifies to τ = pE. This is the expression for the magnitude of the torque when the dipole is perpendicular to the electric field.

Conclude with the final expression: The magnitude of the torque exerted by the electric field on the dipole is τ = pE, where p = qs is the dipole moment and E is the electric field strength.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Electric Dipole

An electric dipole consists of two equal and opposite charges, +q and -q, separated by a distance s. This configuration creates a dipole moment, represented as p = qs, which is a vector quantity pointing from the negative charge to the positive charge. The dipole moment is crucial in understanding how dipoles interact with electric fields.

Torque in Electric Fields

Torque (τ) is a measure of the rotational force acting on an object. In the context of an electric dipole in an electric field, the torque experienced by the dipole is given by the equation τ = p × E, where p is the dipole moment and E is the electric field vector. This relationship shows how the orientation of the dipole relative to the field affects the torque.

Magnitude of Torque

The magnitude of the torque exerted on an electric dipole in an electric field can be expressed as τ = pE sin(θ), where θ is the angle between the dipole moment vector and the electric field vector. This formula indicates that the torque is maximized when the dipole is perpendicular to the field (θ = 90°) and is zero when aligned with the field (θ = 0°).

Recommended video:

Guided course

08:55

Net Torque & Sign of Torque

Related Practice

Textbook Question

Two equal point charges 2.5 cm apart, both initially neutral, are being charged at the rate of 5.0 nC/s. At what rate (N/s) is the force between them increasing 1.0 s after charging begins?

Textbook Question

You have two small, 2.0 g balls that have been given equal but opposite charges, but you don't know the magnitude of the charge. To find out, you place the balls distance apart on a slippery horizontal surface, release them, and use a motion detector to measure the initial acceleration of one of the balls toward the other. After repeating this for several different separation distances, your data are shown below. Use an appropriate graph of the data to determine the magnitude of the charge.

views

Textbook Question

You have a lightweight spring whose unstretched length is 4.0 cm. First, you attach one end of the spring to the ceiling and hang a 1.0 g mass from it. This stretches the spring to a length of 5.0 cm. You then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. This stretches the spring to a length of 4.5 cm. What is the magnitude of the charge (in nC) on each bead?

Textbook Question

Three 1.0 nC charges are placed as shown in FIGURE P22.66. Each of these charges creates an electric field E at a point 3.0 cm in front of the middle charge. What are the three fields E₁, E₂, and E₃ created by the three charges? Write your answer for each as a vector in component form.

Textbook Question

The identical small spheres shown in FIGURE P22.64 are charged to +100 nC and −100 nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

Textbook Question

A 10.0 nC charge is located at position (x, y)=(1.0 cm, 2.0 cm). At what (x, y) position(s) is the electric field $open paren 21 comma 600 i hat minus 28 comma 800 j hat close paren$ N/C?

views