Textbook Question
Three point charges are arranged along the -axis. Charge C is at the origin, and charge C is at m. Charge C. Where is located if the net force on is N in the -direction?
1
views
Ch 21: Electric Charge and Electric Field
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 21, Problem 25a
A proton is traveling horizontally to the right at m/s. Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of cm.
Verified step by step guidance1
First, identify the initial velocity \( v_i \) of the proton, which is given as \( 4.50 \times 10^6 \) m/s, and the final velocity \( v_f \) which is 0 m/s since the proton comes to rest.
Next, note the distance \( d \) over which the proton comes to rest, which is given as 3.20 cm. Convert this distance to meters by dividing by 100, resulting in \( 0.032 \) m.
Use the kinematic equation \( v_f^2 = v_i^2 + 2a d \) to solve for the acceleration \( a \). Rearrange the equation to \( a = \frac{v_f^2 - v_i^2}{2d} \). Substitute the known values to find \( a \).
Recall that the force \( F \) acting on the proton is related to the electric field \( E \) by the equation \( F = qE \), where \( q \) is the charge of the proton (\( 1.60 \times 10^{-19} \) C). Also, \( F = ma \), where \( m \) is the mass of the proton (\( 1.67 \times 10^{-27} \) kg).
Combine the equations \( F = ma \) and \( F = qE \) to solve for the electric field \( E \). Rearrange to \( E = \frac{ma}{q} \). Substitute the values for \( m \), \( a \), and \( q \) to find the magnitude of the electric field. The direction of the electric field will be opposite to the direction of the proton's initial velocity to bring it to rest.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
7mWas this helpful?
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 particle where a force would be exerted on other charged particles. It is represented by the vector E and measured in newtons per coulomb (N/C). The direction of the electric field is the direction of the force it would exert on a positive charge.
Recommended video:
Guided course
03:16
Intro to Electric Fields
Kinematics
Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves equations that relate displacement, velocity, acceleration, and time. In this problem, kinematics helps determine how the proton's velocity changes as it travels through the electric field.
Recommended video:
Guided course
08:25Kinematics Equations
Work-Energy Principle
The work-energy principle states that the work done by forces on an object results in a change in its kinetic energy. For a proton brought to rest, the work done by the electric field equals the initial kinetic energy of the proton. This principle helps calculate the required electric field strength to stop the proton over a given distance.
Recommended video:
Guided course
04:10The Work-Energy Theorem
Related Practice
Textbook Question
A proton is traveling horizontally to the right at m/s. How much time does it take the proton to stop after entering the field?
Textbook Question
A positive charge is fixed at the point , , and a negative charge is fixed at the point , . Show the positions of the charges in a diagram.
Textbook Question
Three point charges are arranged on a line. Charge nC and is at the origin. Charge nC and is at cm. Charge is at cm. What is (magnitude and sign) if the net force on is zero?
Textbook Question
The earth has a net electric charge that causes a field at points near its surface equal to and directed in toward the center of the earth. What magnitude and sign of charge would a -kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field?
Textbook Question
A proton is traveling horizontally to the right at m/s. What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)? Note: Part (a) asks for how much time does it take the proton to stop after entering the field.
1
views