Textbook Question
The electric field strength 1.5 cm from an electric dipole, on the axis of the dipole, is 1.5×105 N/C. If the dipole is replaced by a single charge, what magnitude charge in nC will give the same field strength 1.5 cm away?
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Ch 23: The Electric Field
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 23, Problem 5a
The electric field strength 1.5 cm from an electric dipole, on the axis of the dipole, is 1.5×105 N/C. What is the dipole moment in nC mm?
Verified step by step guidance1
Understand the problem: The electric field strength due to a dipole on its axis is given, and we need to calculate the dipole moment. The formula for the electric field on the axis of a dipole is: , where is the electric field, is Coulomb's constant, is the dipole moment, and is the distance from the dipole center.
Rearrange the formula to solve for the dipole moment : . This will allow us to calculate the dipole moment once we substitute the known values.
Substitute the given values into the formula: The electric field strength is N/C, the distance is cm (convert to meters: m), and Coulomb's constant is approximately N·m²/C².
Perform the unit conversion for the dipole moment: The dipole moment will initially be in units of C·m. To convert to nC·mm, multiply the result by (to convert C to nC) and by (to convert m to mm).
After substituting and simplifying, you will have the dipole moment in nC·mm. Ensure all calculations are consistent with the units and verify the result.
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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 separated by a distance. It is characterized by its dipole moment, which is a vector quantity pointing from the negative charge to the positive charge. The dipole moment (p) is defined as the product of the charge (q) and the separation distance (d), given by p = q × d.
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Intro To Dipole Moment
Electric Field Strength
Electric field strength (E) is a measure of the force experienced by a unit positive charge placed in an electric field. It is expressed in newtons per coulomb (N/C). For an electric dipole, the electric field strength at a point along the axis can be calculated using the formula E = (1/(4πε₀)) * (2p/r³), where p is the dipole moment and r is the distance from the dipole.
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Dipole Moment Calculation
To find the dipole moment from the electric field strength, one can rearrange the formula for electric field due to a dipole. Given the electric field strength and the distance from the dipole, the dipole moment can be calculated as p = (E * 4πε₀ * r³) / 2. The result is often expressed in nanocoulomb millimeters (nC mm) for practical applications.
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Related Practice
Textbook Question
What are the strength and direction of the electric field at the position indicated by the dot in FIGURE EX23.3? Specify the direction as an angle cw from horizontal.
Textbook Question
An electric dipole is formed from two charges, ±q, spaced 1.0 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x, y)=(0 cm, 10 cm) is 360 N/C. What is the charge q? Give your answer in nC.
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Textbook Question
An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0×10−7 C m is 25 cm from a small ball charged to +25 nC, with the ball on the axis of the electric dipole. What is the magnitude of the electric force on the ball?