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?

Work done is directly proportional to potential difference. 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?

The electric field is conservative, making energy independent of path. Signup and view all the answers

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

A circle. Signup and view all the answers

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

The electric potential difference. Signup and view all the answers

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

When the charge does not move. Signup and view all the answers

What is the relationship between electric potential and electric field?

Electric potential is calculated by integrating the electric field. Signup and view all the answers

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

W = QEd 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?

By performing integration between the initial and final points Signup and view all the answers

What signifies a conservative electric field?

The work done is independent of the path taken. Signup and view all the answers

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

Change in potential energy equals the negative of work done. 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?

-50 Joules Signup and view all the answers

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

It gives the magnitude of work when the force is constant. Signup and view all the answers

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

The work done calculated through a specific path. Signup and view all the answers

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

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

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

pv = -8εο C/m³ Signup and view all the answers

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

29.5 V/m Signup and view all the answers

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

D = εοE Signup and view all the answers

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

In an electrostatic field Signup and view all the answers

Which statement accurately describes electric potential difference?

It is defined as the change in electric potential energy per unit charge. Signup and view all the answers

How is the electric potential at point P calculated?

VP = 4(-2)²(1) - 3(-2)(1) + 5(4) Signup and view all the answers

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

Electric field points in the direction of decreasing potential. Signup and view all the answers

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 = Q⋅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 ⋅ 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 = ∫_a^bE⋅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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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.