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Chapter 20: Problem 71

A proton is released from rest in a region of space with a nonzero electric field. As the proton moves, does it experience an increasing or decreasing electric potential? Explain.

Short Answer

Expert verified
The proton experiences a decreasing electric potential as it moves in the field.

Step by step solution

01

Understanding Electric Potential

Electric potential, often denoted as \( V \), is a scalar quantity that represents the potential energy per unit charge at a point in an electric field. It is directly related to the work done by an electric field in moving a charge from one point to another.
02

Proton Characteristics

A proton is a positively charged particle. When it is released in an electric field, it will move due to the force exerted on it by the electric field. The direction of this force is the same as the direction of the electric field because the charge of the proton is positive.
03

Movement of Proton in the Electric Field

Since the proton is positively charged and moves in the direction of the electric field, it moves towards the region of lower electric potential. This is because moving along the direction of the electric field corresponds to moving down the potential gradient, similar to how objects move downhill along a gravitational field.
04

Decreasing Electric Potential

As the proton moves in the direction of the electric field (which is the direction of decreasing potential), it experiences a decrease in electric potential. The potential energy of the proton decreases because it is gaining kinetic energy as it moves.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Field
An electric field is a fundamental concept in physics. It represents the force that a charged particle would experience at any given point in space. This field is depicted as a series of lines that indicate the direction of the force: from positive to negative charges. When a charge is placed in an electric field, it experiences a force based on the field's strength and the charge's magnitude.
The electric field ( \( E \) ) is defined as the force ( \( F \) ) per unit charge ( \( q \) ), so \( E = \frac{F}{q} \) .
  • The direction of the field: From positive to negative.
  • Force on positive charge: Along the field lines.
  • Force on negative charge: Opposite the field lines.
This field energy can push or pull charges into motion, impacting their potential and kinetic energies.
Proton Characteristics
A proton is one of the basic building blocks of atoms. It is found in the nucleus along with neutrons and is positively charged, with a charge equal to \(+1.6 \times 10^{-19} \text{C} \).
Being positively charged, protons interact strongly with electric fields.
  • Protons move in the direction of the electric field because they are positive.
  • The mass of a proton is approximately \(1.67 \times 10^{-27} \text{kg} \).
Protons are subject to forces exerted by electric fields, which influence how they move and change energies. This movement through a field affects their energy levels, transitioning potential energy into kinetic energy.
Potential Energy
Potential energy in an electric field represents the stored energy due to the position of a charged particle within the field. It is important to understand that potential energy changes as the charge moves.
The potential energy ( \( U \) ) of a charge ( \( q \) ) within an electric potential ( \( V \) ) is defined as:\[ U = qV \]
  • Positive charges move from high to low potential, decreasing potential energy.
  • Negative charges move from low to high potential, increasing potential energy.
As a proton moves in the electric field, its potential energy decreases, indicating a conversion into kinetic energy due to the field's work.
Kinetic Energy
Kinetic energy is the energy that a particle possesses due to its motion. In the context of a proton in an electric field, as the proton accelerates, its kinetic energy increases.
Whenever potential energy decreases, kinetic energy often increases, since energy is conserved unless disturbed by external factors.
The formula for kinetic energy ( \( KE \) ) is:\[ KE = \frac{1}{2}mv^2 \]where \( m \) is the mass, and \( v \) is the velocity of the particle.
  • The proton's motion is caused by the electric force acting on it.
  • This motion transforms potential energy into kinetic energy.
This energy interchange shows how forces within electric fields guide the conversion of energy, influencing the dynamics of charge motion.

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Most popular questions from this chapter

Electric Potential Across a Cell Membrane In a typical living cell, the electric potential inside the cell is \(0.070 \mathrm{V}\) lower than the electric potential outside the cell. The thickness of the cell membrane is \(0.10 \mu \mathrm{m}\). What are the magnitude and direction of the electric field within the cell membrane?

A charge of \(20.2 \mu C\) is held fixed at the origin. (a) If a \(-5.25-\mu C\) charge with a mass of \(3.20 \mathrm{g}\) is released from rest at the position \((0.925 \mathrm{m}, 1.17 \mathrm{m}),\) what is its speed when it is halfway to the origin? (b) Suppose the \(-5.25-\mu \mathrm{C}\) charge is released from rest at the point \(x=\frac{1}{2}(0.925 \mathrm{m})\) and \(y=\frac{1}{2}(1.17 \mathrm{m}) .\) When it is halfway to the origin, is its speed greater than, less than, or equal to the speed found in part (a)? Explain. (c) Find the speed of the charge for the situation described in part (b).

The plates of a parallel-plate capacitor have constant charges of \(+Q\) and \(-Q\). Do the following quantities increase, decrease, or remain the same as the separation of the plates is increased? (a) The electric field between the plates; (b) the potential difference between the plates; (c) the capacitance; (d) the energy stored in the capacitor.

It is desired that \(5.8 \mu \mathrm{C}\) of charge be stored on each plate of a \(3.2-\mu \mathrm{F}\) capacitor. What potential difference is required between the plates?

Cell Membranes The membrane of a living cell can be approximated by a parallel-plate capacitor with plates of area \(4.75 \times 10^{-9} \mathrm{m}^{2},\) a plate separation of \(8.5 \times 10^{-9} \mathrm{m},\) and a dielectric with a dielectric constant of \(4.5 .\) (a) What is the energy stored in such a cell membrane if the potential difference across it is \(0.0725 \mathrm{V}\) ? (b) Would your answer to part (a) increase, decrease, or stay the same if the thickness of the cell membrane is increased? Explain.
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