Physics Chapter 5: Electric Potential
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Questions and Answers

What does a positive work value signify in the context of moving a charge in an electric field?

  • It indicates an increase in system energy. (correct)
  • It signifies no change in energy.
  • It indicates a decrease in system energy.
  • It denotes that work done is zero.

The line integral for work done in moving a charge is defined as W = -Q∫E · dl. What does the negative sign signify?

  • Work done by the electric field is always positive.
  • It reverses the direction of the work calculation.
  • It is a mathematical formality with no physical meaning.
  • It indicates work done against the electric field. (correct)

In the calculation of work done in an electric field, which integral vanishes due to equal limits?

  • ∫_A^B 5dz (correct)
  • ∫_A^B Edl
  • ∫_A^B xdy
  • ∫_A^B ydx

When moving a charge in an electric field, what is the relationship between work done and electric potential difference?

<p>Work done is directly proportional to potential difference. (B)</p> Signup and view all the answers

Why does the work done in transferring a charge from A to B along different paths yield the same result in a conservative electric field?

<p>The electric field is conservative, making energy independent of path. (B)</p> Signup and view all the answers

What shape can be described by the equation x² + y² = 25?

<p>A circle. (B)</p> Signup and view all the answers

What does the change in electric potential energy per unit charge represent in an electric field?

<p>The electric potential difference. (C)</p> Signup and view all the answers

In which scenario would the work done on a charge be zero?

<p>When the charge does not move. (C)</p> Signup and view all the answers

What is the relationship between electric potential and electric field?

<p>Electric potential is calculated by integrating the electric field. (C)</p> Signup and view all the answers

Which equation correctly describes the work done on a charged particle by an electric field?

<p>W = QEd (B)</p> Signup and view all the answers

In a situation where the force acting on a charged particle is variable, how is the work done calculated?

<p>By performing integration between the initial and final points (C)</p> Signup and view all the answers

What signifies a conservative electric field?

<p>The work done is independent of the path taken. (B)</p> Signup and view all the answers

How is the change in electric potential energy related to the work done on the charge?

<p>Change in potential energy equals the negative of work done. (D)</p> Signup and view all the answers

If a uniform electric field does 50 Joules of work on a charge, what is the change in electric potential energy of the system?

<p>-50 Joules (C)</p> Signup and view all the answers

Which of the following best describes the dot product of force and displacement?

<p>It gives the magnitude of work when the force is constant. (C)</p> Signup and view all the answers

In the context of electric fields, what does the notation W = ∫F · dl represent?

<p>The work done calculated through a specific path. (D)</p> Signup and view all the answers

What is the correct expression for electric field E as derived from the potential function V?

<p>E = -[(8xy - 3y)ax + (4x² - 3x)ay + 5az] (A)</p> Signup and view all the answers

What is the charge density at point P if the divergence of D is given as -8εοy?

<p>pv = -8εο C/m³ (C)</p> Signup and view all the answers

What is the magnitude of the electric field E at point P?

<p>29.5 V/m (D)</p> Signup and view all the answers

The electric flux density D is expressed as which of the following?

<p>D = εοE (A)</p> Signup and view all the answers

In which case does the work done in moving a charge around a closed path equal zero?

<p>In an electrostatic field (A)</p> Signup and view all the answers

Which statement accurately describes electric potential difference?

<p>It is defined as the change in electric potential energy per unit charge. (D)</p> Signup and view all the answers

How is the electric potential at point P calculated?

<p>VP = 4(-2)²(1) - 3(-2)(1) + 5(4) (D)</p> Signup and view all the answers

What does the negative gradient of the potential function indicate about the electric field?

<p>Electric field points in the direction of decreasing potential. (A)</p> Signup and view all the answers

Flashcards

Work done in an electric field

The work needed to move a charge through an electric field, calculated by integrating the electric field vector along the path of the charge.

Electric potential difference

The change in electric potential energy per unit charge between two points in an electric field.

Conservative field

An electric field where the work done to move a charge between two points is independent of the path taken.

Equation for work calculation (electric field)

W = -Q∫E · dl, where W is work, Q is the charge, E is the electric field, and dl is an infinitesimal displacement along the path.

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Calculating work (conservative)

For conservative fields, the work is equivalent to the product of the charge and the potential difference ΔV: W = Q·ΔV.

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Line integral

The process of integrating quantities over a trajectory (path) in an area or space (like an electrical field).

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Potential difference calculation

VAB = -∫BAE · dl, the potential difference between two points is calculated using the line integral of the electric field.

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Work in Problem 5.1 or Problem 5.2

The work was calculated by integrating a non-uniform electric field along a path. The work done along a circle path and a straight line path in the problem were the same.

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Electric Potential

A scalar quantity describing the potential energy per unit charge in an electric field.

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Work in an Electric Field

Work done by the force when a charge moves within an electric field.

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Electric Potential Energy Change

The difference in potential energy of a charge when moved in an electric field.

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Uniform Electric Field Work

Work done in a uniform electric field, calculated using QEd.

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Calculating Work (Variable Field)

Work in a varying electric field is calculated by integrating the electric field along the path.

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Work as a Dot Product

Work done in any electric field, calculated as the dot product of force and displacement.

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Relationship between Electric Field and Potential

Electric potential can be used to determine the electric field via differentiation (rather than integration), in many cases offering a simpler calculation.

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Electric Potential at a Point

The amount of work required to move a unit positive charge from infinity to that point in an electric field.

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Electric Field and Potential Relationship

The electric field is the negative gradient of the electric potential. This means the electric field points in the direction of the steepest decrease in potential.

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Electric Flux Density

A measure of the electric field strength per unit area. It represents the number of electric field lines passing through a unit area.

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Charge Density and Divergence of Electric Flux Density

The charge density at a point is equal to the divergence of the electric flux density at that point. This relates the distribution of charges to the electric field.

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Potential of a Charged Ring

The electric potential at a point on the axis of a uniformly charged ring is calculated using the Coulomb's law and integrating over the ring's charge distribution.

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Potential of an Infinite Line Charge

The potential of an infinite line charge with uniform charge density is inversely proportional to the distance from the line. This potential is calculated using integration along the line.

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Work Done in Moving a Charge

The work done in moving a point charge in an electric field is calculated using the line integral of the electric field along the path of the charge. For conservative fields, work is the charge times the potential difference.

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Study Notes

Chapter 5: Electric Potential

  • Electric fields calculated using Coulomb's law and Gauss's law
  • Electric potential, a scalar quantity, is easier to work with than electric forces and fields
  • Potential function allows for calculation of electric fields through differentiation
  • The voltage is a familiar concept related to electric potential
  • Electrostatic fields are conservative
  • Maxwell's equations can be derived from properties of electrostatic fields

Work Done by an Electric Field

  • A charged particle in an electric field experiences a force (F = Qâ‹…E)
  • Work is done when the charge moves due to the force
  • Work (W) is equal to the dot product of force and displacement (W = F â‹… d)
  • W = QEd, where E is uniform
  • Work done on a charge is internal to the system
  • Work done to move a charge requires energy
  • Work done is independent of path in a conservative field

Electric Potential Difference

  • The work done moving a charge between two points in an electric field equals the change in the electric potential energy of the system, regardless of the path.
  • Electric potential difference (VAB) is a scalar quantity
  • VAB is defined as the change in potential energy per unit charge in moving a unit positive test charge between two points
  • VAB = ∫abEâ‹…dl (Potential difference between points a and b)
  • The potential at a point is the work done per unit charge in bringing a unit positive test charge from a point of zero potential to that point.
  • Electric potential is usually taken to be zero at infinity.

Illustrative Problems

  • Various examples demonstrate calculating work and potential differences between two points due to sources such as point or line charges. A variety of problem-solving steps including calculus are used.

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Electric Potential PDF

Description

Explore the concepts of electric potential and fields in this quiz based on Chapter 5 of your physics curriculum. Test your understanding of Coulomb's law, work done by electric fields, and the relationship between voltage and electric potential. Assess your grasp on the derivation of Maxwell's equations through electrostatic principles.

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