Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 15th Edition

Ch 21: Electric Charge and Electric Field

문제 20a

21장, 문제 20a

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, $1.60$ cm distant from the first, in a time interval of $3.20 \times 10^{- 6}$ s. Find the magnitude of the electric field.

검증된 단계별 안내

Start by understanding the motion of the proton. Since it is released from rest, its initial velocity is zero. The proton is accelerated by the electric field between the plates.

Use the kinematic equation for uniformly accelerated motion:

d = v

₀t + 12at², where

d

is the distance,

v

₀ is the initial velocity,

a

is the acceleration, and

t

is the time.

Since the initial velocity

v

₀ is zero, the equation simplifies to

d = \frac{1}{2} a t

². Plug in the given values:

= 1.60 imes 10^{-2} \(\text{ m}\)

and

= 3.20 imes 10^{-6} \(\text{ s}\)

Solve for acceleration

a

using the equation:

a = rac{2 d}{t

²}. Substitute the values to find

a

Relate the acceleration to the electric field using the formula

a = rac{q E}{m}

, where

q

is the charge of the proton and

m

is the mass of the proton. Rearrange to solve for the electric field

E

E = rac{m a}{q}

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Electric Field

An electric field is a region around a charged object where other charged objects experience a force. It is represented by the vector quantity E, which indicates the force per unit charge. In this scenario, the uniform electric field between the plates exerts a constant force on the proton, influencing its motion.

Kinematics

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. To solve this problem, we use kinematic equations to relate the proton's initial velocity, acceleration due to the electric field, distance traveled, and time taken to reach the opposite plate.

Force on a Charged Particle

The force on a charged particle in an electric field is given by F = qE, where q is the charge of the particle and E is the electric field strength. For a proton, this force causes acceleration, which can be calculated using Newton's second law, F = ma, allowing us to determine the electric field's magnitude.