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 33

25장, 문제 33

Two small charged spheres are 5.0 cm apart. One is charged to +25 nC, the other to −15 nC. A proton is released from rest halfway between the spheres. What is the proton's speed after it has moved 1.0 cm?

검증된 단계별 안내

Step 1: Calculate the electric field at the midpoint between the two spheres due to each charge. Use the formula for the electric field due to a point charge:

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

, where

k

is Coulomb's constant,

q

is the charge, and

r

is the distance from the charge to the point of interest.

Step 2: Determine the net electric field at the midpoint by adding the contributions from both charges. Remember that the electric field vectors will point away from positive charges and toward negative charges, so their directions must be considered when summing.

Step 3: Calculate the force acting on the proton due to the net electric field using the formula:

F = q E

, where

q

is the charge of the proton and

E

is the net electric field.

Step 4: Use Newton's second law to find the acceleration of the proton:

a = \frac{F}{m}

, where

F

is the force and

m

is the mass of the proton.

Step 5: Use kinematic equations to calculate the proton's speed after it has moved 1.0 cm. Use the equation:

v^{2} = v^{0} + 2 a d

, where

v

is the final speed,

v 0

is the initial speed (zero in this case),

a

is the acceleration, and

d

is the distance moved (1.0 cm).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the forces acting on the proton due to the charged spheres.

Electric Potential Energy

Electric potential energy is the energy a charged particle possesses due to its position in an electric field. It is calculated based on the charges involved and their separation distance. Understanding how potential energy changes as the proton moves is crucial for determining its speed after moving 1.0 cm.

Kinematics and Energy Conservation

Kinematics involves the study of motion, while energy conservation principles state that the total mechanical energy in a closed system remains constant. In this scenario, the potential energy lost by the proton as it moves will convert into kinetic energy, allowing us to calculate its speed after moving a certain distance.