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 30

23장, 문제 30

A proton is fired horizontally into a 1.0×10⁵ N/C vertical electric field. It rises 1.0 cm vertically after having traveled 5.0 cm horizontally. What was the proton's initial speed?

검증된 단계별 안내

Step 1: Identify the forces acting on the proton. The proton is subject to an electric force due to the vertical electric field. The electric force can be calculated using the formula:

F = q E

, where

q

is the charge of the proton and

E

is the electric field strength.

Step 2: Determine the acceleration of the proton due to the electric force. Using Newton's second law,

a = \frac{F}{m}

, where

m

is the mass of the proton, substitute

F = q E

to find the vertical acceleration.

Step 3: Use kinematic equations to relate the vertical displacement to the vertical acceleration. The vertical displacement

y

is given as 1.0 cm (convert to meters: 0.01 m). Using the equation

y = \frac{1}{2} a t^2

, solve for the time

t

it takes for the proton to rise 1.0 cm.

Step 4: Relate the horizontal motion to the time of flight. The horizontal displacement

x

is given as 5.0 cm (convert to meters: 0.05 m). Using the equation

x = v t

, where

v

is the initial horizontal speed, solve for

v

using the time

t

found in Step 3.

Step 5: Combine the results from Steps 2, 3, and 4 to calculate the initial speed of the proton. Ensure all units are consistent throughout the calculations (e.g., meters, seconds, etc.).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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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 particle where other charged particles experience a force. The strength of an electric field is measured in newtons per coulomb (N/C) and indicates how much force a unit charge would experience. In this problem, the vertical electric field exerts a force on the proton, causing it to rise as it moves horizontally.

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject to gravitational and other forces. In this scenario, the proton's horizontal motion is uniform while its vertical motion is influenced by the electric field. Understanding the components of projectile motion helps in analyzing the proton's trajectory and calculating its initial speed.

Kinematics Equations

Kinematics equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, these equations are essential for determining the proton's initial speed based on its vertical rise and horizontal travel, allowing us to connect the forces acting on it to its motion.

관련 실천

교과서 질문

FIGURE EX23.25 shows a $1.5$ g ball hanging from a string inside a parallel-plate capacitor made with 12 cm × 12 cm electrodes. The electrodes are charged to±75 nC. What is the charge on the ball in nC?

Electrostatic cleaners remove small dust particles and pollen grains from air by first ionizing them, then flowing the air between the plates of a parallel-plate capacitor, parallel to the plates, where electric forces deposit charged particles on one of the electrodes. A typical pollen grain has a mass of $5.0 \times 10^{- 10}$ g, the ionizer charges it with $750$ extra electrons, and a fan moves the air at $3.0$ m/s. Ignore air resistance and gravity. What minimum electric field strength is needed to deflect the grain by $3.0$ mm before it leaves the electrodes?

1923

views

교과서 질문

What are the strength and direction of the electric field at the position indicated by the dot in FIGURE P23.37? Give your answer (a) in component form and (b) as a magnitude and angle measured cw or ccw (specify which) from the positive x-axis.

210

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교과서 질문

Two 2.0-cm-diameter disks face each other, 1.0 mm apart. They are charged to ±10 nC. A proton is shot from the negative disk toward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

202

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교과서 질문

INT The surface charge density on an infinite charged plane is −2.0×10⁻⁶ C/m². A proton is shot straight away from the plane at 2.0×10⁶ m/s. How far does the proton travel before reaching its turning point?

2301

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교과서 질문

The permanent electric dipole moment of the water molecule (H₂O) is $6.2 \times 10^{- 30}$ Cm. What is the maximum possible torque on a water molecule in a $5.0 \times 10^{8}$ N/C electric field?

2672

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A proton is fired horizontally into a 1.0×105 N/C vertical electric field. It rises 1.0 cm vertically after having traveled 5.0 cm horizontally. What was the proton's initial speed?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Electric Field

Projectile Motion

Kinematics Equations

A proton is fired horizontally into a 1.0×10⁵ N/C vertical electric field. It rises 1.0 cm vertically after having traveled 5.0 cm horizontally. What was the proton's initial speed?