Ch 25: The Electric Potential

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 25: The Electric Potential

문제 7

25장, 문제 7

Two positive point charges are 5.0 cm apart. If the electric potential energy is 72 μJ, what is the magnitude of the force between the two charges?

검증된 단계별 안내

Step 1: Recall the formula for electric potential energy between two point charges:

U = \frac{k q q}{r}

, where

U

is the electric potential energy,

k

is Coulomb's constant (

8.99×10

⁹ N·m²/C²),

q

and

q

are the charges, and

r

is the distance between them.

Step 2: Rearrange the formula to solve for the product of the charges

q q

q q = \frac{U r}{k}

. Substitute the given values:

U

= 72 μJ =

72×10

^-6 J,

r

= 5.0 cm =

0.050 m

, and

k

8.99×10

⁹ N·m²/C².

Step 3: Recall the formula for the magnitude of the force between two point charges:

F = \frac{k q q}{r^{2}}

. Substitute the value of

q q

obtained from Step 2 into this formula.

Step 4: Substitute the known values for

k

and

r

into the force formula. Ensure that the distance

r

is squared in the denominator.

Step 5: Perform the calculations step by step to find the magnitude of the force

F

. Ensure units are consistent throughout the calculation (e.g., meters for distance, joules for energy).

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주요 개념

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

Electric Potential Energy

Electric potential energy is the energy stored in a system of charged particles due to their positions relative to each other. It is given by the formula U = k * (q1 * q2) / r, where U is the potential energy, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. In this case, the potential energy of 72 μJ indicates the work done to assemble the two charges at a distance of 5.0 cm.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force F between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, expressed as F = k * (q1 * q2) / r². This law is fundamental in calculating the force when the charges and distance are known.

Relationship Between Force and Potential Energy

The relationship between electric potential energy and force can be understood through the concept of work. The force acting between two charges can be derived from the potential energy by using the formula F = -dU/dr, where dU is the change in potential energy and dr is the change in distance. This relationship allows us to calculate the force when the potential energy and distance are known, linking the two concepts effectively.