Ch 23: The Electric Field

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 23: The Electric Field

문제 5a

23장, 문제 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?

검증된 단계별 안내

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:

E = \frac{2 k p}{r^{3}}

, where

E

is the electric field,

k

is Coulomb's constant,

p

is the dipole moment, and

r

is the distance from the dipole center.

Rearrange the formula to solve for the dipole moment

p

p = \frac{E r^{3}}{2}

. 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

1.5 × 10^{5}

N/C, the distance

r

1.5

cm (convert to meters:

0.015

m), and Coulomb's constant

k

is approximately

8.99 × 10^{9}

N·m²/C².

Perform the unit conversion for the dipole moment: The dipole moment

p

will initially be in units of C·m. To convert to nC·mm, multiply the result by

10

⁹ (to convert C to nC) and by

1000

(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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.