Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 21: Electric Charge and Electric Field

Problem 20a

Chapter 21, Problem 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.

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

Three point charges are arranged along the $x$ -axis. Charge $q sub 1 equals positive 3.00$ $μ$ C is at the origin, and charge $q_{2} = - 5.00$ $μ$ C is at $x equals 0.200$ m. Charge $q_{2} = - 8.00$ $μ$ C. Where is $q sub 3$ located if the net force on $q sub 1$ is $7.00$ N in the $- x$ -direction?

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Textbook Question

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 speed of the proton when it strikes the negatively charged plate.

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Textbook Question

A proton is traveling horizontally to the right at $4.50$\times$10^6$ m/s. How much time does it take the proton to stop after entering the field?

Textbook Question

Three point charges are arranged on a line. Charge $q sub 3 equals positive 5.00$ nC and is at the origin. Charge $q_{2} = - 3.00$ nC and is at $x equals positive 4.00$ cm. Charge $q sub 1$ is at $x equals positive 2.00$ cm. What is $q sub 1$ (magnitude and sign) if the net force on $q sub 3$ is zero?

Textbook Question

A proton is traveling horizontally to the right at $4.50 \times 10^{6}$ m/s. Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of $3.20$ cm.

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Textbook Question

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4$\times$10^{-15}$ m. What magnitude of electric field does it produce at the distance of the electrons, which is about $1.0 \times 10^{- 10}$ m?

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