Electric Fields and Potential Energy

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Questions and Answers

If the electric field is directed downward, how does the electric potential at point B relate to the electric potential at point A?

  • Points A and B have the same electric potential
  • Point B is at a lower potential than point A (correct)
  • Point B is at a higher potential than point A
  • The electric potential at point B could be higher or lower than at point A, depending on the magnitude of the electric field.

What happens to the potential energy of a charge-field system when a positive test charge moves in the direction of the electric field?

  • The potential energy oscillates.
  • The potential energy increases.
  • The potential energy remains constant.
  • The potential energy decreases. (correct)

A system consists of a positive charge and an electric field. When does the system lose electric potential energy?

  • When the charge moves against the direction of the field
  • When the charge oscillates perpendicular to the field
  • When the charge remains stationary
  • When the charge moves in the direction of the field (correct)

As a charged particle moves in an electric field, what form of energy does it gain, which is equal to the loss of potential energy of the charge-field system?

<p>Kinetic energy (B)</p> Signup and view all the answers

A system consists of a negative charge and an electric field. When does the system gain potential energy?

<p>When the charge moves in the direction of the field (A)</p> Signup and view all the answers

For a negative charge to move in the direction of the electric field, what must occur?

<p>An external agent must do positive work on the charge (A)</p> Signup and view all the answers

When a test charge is placed in an electric field, it experiences a force. What is the nature of this force?

<p>Conservative (D)</p> Signup and view all the answers

If a test charge is moved in an electric field by an external agent, how does the work done by the field relate to the work done by the external agent?

<p>The work done by the field is the negative of the work done by the external agent. (A)</p> Signup and view all the answers

What does the infinitesimal displacement vector, $d\vec{s}$, represent in the context of electric potential energy?

<p>A vector oriented tangent to a path through space (B)</p> Signup and view all the answers

The work done by the electric field is expressed as $\vec{F} \cdot d\vec{s} = q_0 \vec{E} \cdot d\vec{s}$. What does this expression calculate?

<p>The infinitesimal work done on a charge $q_0$ by the electric field $\vec{E}$ over a displacement $d\vec{s}$ (B)</p> Signup and view all the answers

The change in potential energy within an electric field is given by $\Delta U = -q_0 \int_A^B \vec{E} \cdot d\vec{s}$. What does this equation calculate?

<p>The change in potential energy of the charge $q_0$ as it moves from point A to point B in the electric field $\vec{E}$ (D)</p> Signup and view all the answers

Why is the line integral used to calculate the work done by a conservative force independent of the path taken by the charge?

<p>The force depends only on the initial and final positions of the charge. (D)</p> Signup and view all the answers

The electric potential is defined as the potential energy per unit charge. Which statement accurately describes the nature of electric potential?

<p>It is characteristic of the field only (C)</p> Signup and view all the answers

Which of the following is NOT true about electric potential?

<p>It is a vector quantity (C)</p> Signup and view all the answers

How will a charged particle behave when it moves in an electric field?

<p>It will experience a change in potential (C)</p> Signup and view all the answers

What is the important quantity associated with electric potential?

<p>The difference in potential between two points (C)</p> Signup and view all the answers

In practical applications involving electric potential, what is often assumed about the value of the potential at a convenient point in the field?

<p>It is set to zero. (D)</p> Signup and view all the answers

What characteristic defines electric potential in relation to charges that may be placed in the field?

<p>It is a scalar characteristic, independent of any charges placed in the field. (D)</p> Signup and view all the answers

If a charge moves in an electric field without any change in its kinetic energy, what equation expresses the work performed on the charge?

<p>$W = \Delta U = q \Delta V$ (B)</p> Signup and view all the answers

What is the definition of a volt (V) in terms of other SI units?

<p>1 V = 1 Joule / Coulomb (D)</p> Signup and view all the answers

What amount of work is required to move a 1-coulomb charge through a potential difference of 1 volt?

<p>1 Joule (D)</p> Signup and view all the answers

In atomic and nuclear physics, what unit of energy is commonly used in addition to the joule?

<p>The electron-volt (D)</p> Signup and view all the answers

How is one electron-volt defined?

<p>The energy gained or lost by a charge of magnitude <em>e</em> moving through a potential difference of 1 volt (D)</p> Signup and view all the answers

What is the energy equivalent of 1 eV in joules?

<p>1 eV = 1.60 x 10^-19 J (D)</p> Signup and view all the answers

If a positive charge is released from rest in a uniform electric field, in which direction does it move?

<p>In the direction of the electric field (B)</p> Signup and view all the answers

When a positive charge moves in the direction of the electric field, what is the sign of the change in potential?

<p>Negative (D)</p> Signup and view all the answers

How are the force and acceleration related to the direction of the electric field for a positive charge placed within it?

<p>The force and acceleration are in the direction of the field (C)</p> Signup and view all the answers

What principle can be used to determine the speed of a charged particle in a uniform electric field?

<p>Conservation of Energy (D)</p> Signup and view all the answers

If the electric field is uniform, how can the equations for electric potential be simplified?

<p>By considering the electric field to be constant (B)</p> Signup and view all the answers

The equation for the potential difference in a uniform field is given by $V_B - V_A = \Delta V = - \int_A^B \vec{E} \cdot d\vec{s} = -E \int_A^B ds = -Ed$. What does the negative sign in this equation indicate?

<p>The electric potential at point B is lower than at point A (C)</p> Signup and view all the answers

What is the relationship between electric field lines and electric potential?

<p>Electric field lines always point in the direction of decreasing electric potential (D)</p> Signup and view all the answers

What type of field is produced around a positive point charge?

<p>A field directed radially outward (B)</p> Signup and view all the answers

Given two points A and B in the vicinity of a point charge, the potential difference between them is expressed as $V_B - V_A = k_e q [\frac{1}{r_B} - \frac{1}{r_A}]$. What does this formula imply about the electric potential?

<p>It is independent of the path between points A and B. (D)</p> Signup and view all the answers

In the context of electric potential due to a point charge, what is the customary reference point for zero potential?

<p>At infinity (C)</p> Signup and view all the answers

The electric potential at some point r due to a point charge is given by $V = k_e \frac{q}{r}$. What does this equation imply about the potential's dependence on distance?

<p>The potential decreases inversely with distance (B)</p> Signup and view all the answers

How is the electric potential due to several point charges determined?

<p>By summing the potentials due to each individual charge (D)</p> Signup and view all the answers

In calculating the electric potential due to multiple charges, what principle is applied?

<p>The superposition principle (C)</p> Signup and view all the answers

In the context of electric potential with multiple charges, what type of sum is used to calculate the total potential?

<p>An algebraic sum (A)</p> Signup and view all the answers

What is the electric potential at $r = \infty$?

<p>$V = 0$ (B)</p> Signup and view all the answers

For a system of two charged particles, if both charges are of the same sign, what can be said about the potential energy U of the system?

<p><em>U</em> is positive (A)</p> Signup and view all the answers

Under what circumstance is the potential energy U negative?

<p>When the two charges have opposite signs. (A)</p> Signup and view all the answers

The potential energy of a system with three charges is given by $U = k_e (\frac{q_1q_2}{r_{12}} + \frac{q_1q_3}{r_{13}} + \frac{q_2q_3}{r_{23}})$. What does the result from this equation being independent of?

<p>The order of the charges. (A)</p> Signup and view all the answers

Consider three charges, $q_1 = 1,\mu C$, $q_2 = -2,\mu C$, and $q_3 = 3,\mu C$, positioned at the vertices of an equilateral triangle with sides of length $r = 0.1,m$. What is the potential energy of this configuration, and without performing calculations, deduce how its sign will affect the work needed to disassemble the system?

<p>$U = 9.0,J$; positive work is needed to disassemble the system. (D)</p> Signup and view all the answers

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Flashcards

Electric potential and field direction

Point B is at a lower electric potential than point A if the electric field is directed downward.

Positive charge in a field

When a positive charge moves in the direction of the electric field, the charge-field system loses potential energy.

System losing potential energy

When a system consisting of a positive charge and an electric field loses electric potential energy, the charge moves in the direction of the field.

System gains potential energy

For a system consisting of a negative charge and an electric field, the system gains potential energy when the charge moves in the direction of the field.

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Test charge in electric field

When a test charge is placed in an electric field, it experiences a force. This force is conservative.

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Work and external agent

The work done by the electric field is the negative of the work done by the external agent.

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Electric force is conservative

The line integral is independent of the path taken by the charge.

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Electric Potential Definition

Electric potential is the potential energy per unit charge.

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Electric Potential Type

Electric potential is a scalar quantity.

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Scalar characteristic of electric field

Electric potential is a scalar characteristic of an electric field, independent of any charges that may be placed in the field.

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What is a Volt

It takes one joule of work to move a 1-coulomb charge through a potential difference of 1 volt.

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Electron-Volt

One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude e is moved through a potential difference of 1 volt.

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Uniform field, positive charge

The force and acceleration are in the direction of the field and the change in potential is negative.

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Electric field direction

Electric field lines always point in the direction of decreasing electric potential

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Field of postive charge

A positive point charge produces a field directed radially outward

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Electric potential

The electric potential is independent of the path between points A and B

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Potential from multiple charges

The electric potential due to several point charges is the sum of the potentials due to each individual charge.

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Charges with the same sign

If the two charges are the same sign, U is positive and work must be done to bring the charges together.

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Find the Total Potential Energy

If there are more than two charges, then find U for each pair of charges and add them

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Study Notes

Energy and Electric Fields

  • When an electric field points downward, a point B is at a lower potential than a point A above it.
  • When a positive test charge moves from point A to point B, the charge-field system loses potential energy.

Directions of Electric Fields

  • A system composed of a positive charge and an electric field loses electric potential energy when the charge moves with the field.
  • An electric field does work on a positive charge when the charge moves in the direction of the electric field.
  • A charged particle gains kinetic energy equal to the potential energy lost by the charge-field system, as per the Conservation of Energy principle.
  • If qo is negative, then the change in potential energy, ΔU, is positive.
  • A system containing a negative charge and an electric field gains potential energy when the charge moves with the field.
  • Negative charges requires an external agent to do positive work on the charge to move in the direction of the field.

Electrical Potential Energy

  • A test charge placed in an electric field experiences a force.
  • The force is defined as vector F = q₀E, where q₀ is the charge and E is the electric field.
  • This force is conservative.
  • If a test charge is moved within the field by an external agent, the work done by the field is the negative of the work done by the external agent.
  • ds is an infinitesimal displacement vector tangent to the path through space.
  • The work done by the electric field is given by F⋅ds = q₀E⋅ds.
  • As work is done by the field, the potential energy of the charge-field system changes by ΔU = -q₀∫E⋅ds.
  • For a finite displacement of a charge from point A to B, the change in potential energy is ΔU = UB - UA = -q₀∫(from A to B) E⋅ds.
  • The line integral is independent of the path taken by the charge because the force is conservative.
  • The line integral represents the change in potential energy of the system.

Electric Potential

  • Electric potential is the potential energy per unit charge, or U/q₀.
  • The potential is characteristic of the field only.
  • Potential energy is characteristic of the charge-field system
  • The potential is independent of the charge, q₀.
  • Electric potential has a value at every point in an electric field.
  • Electric potential is defined as V = U/q₀.
  • Electric potential is a scalar quantity.
  • Energy is a scalar.
  • A charged particle moving in an electric field experiences a change in potential: ΔV = ΔU/q₀ = -∫(from A to B) E⋅ds.
  • The difference in potential is the important quantity.
  • The value of the potential can be zero at some convenient point in the field.
  • Electric potential is a scalar characteristic of an electric field, independent of any charges placed in the field.

Work

  • If a charge moves in an electric field without any change in its kinetic energy, the work performed on the charge is W = ΔU = qΔV.

Units

  • 1 Volt (V) = 1 Joule per Coulomb (J/C).
  • V is a Volt.
  • It takes one joule of work to move a 1-coulomb charge through a potential difference of 1 volt.

Electron-Volts

  • The electron-volt is a unit of energy commonly used in atomic and nuclear physics.
  • One electron-volt is the energy a charge-field system gains or loses when a charge of magnitude e (an electron or a proton) is moved through a potential difference of 1 volt.
  • 1 eV = 1.60 x 10⁻¹⁹ J.

Uniform Electric Fields

  • In a uniform field, a positive charge is released from rest and moves in the direction of the electric field.
  • The change in potential is negative.
  • The change in potential energy is negative.
  • The force and acceleration are in the direction of the field.
  • Conservation of Energy can be used to find its speed.
  • The equations for electric potential are simplified if the electric field is uniform.
  • VB - VA = ΔV = -∫(from A to B) E⋅ds = -E∫(from A to B) ds = -Ed
  • The negative sign indicates the electric potential at point B is lower than at point A.
  • Electric field lines always point in the direction of decreasing electric potential.

Point Charges

  • A positive point charge produces a field directed radially outward.
  • The potential difference between points A and B is VB - VA = keq [1/rB - 1/rA].
  • Electric potential is independent of the path between points A and B.
  • It is customary to choose a reference potential of V = 0 at rA = ∞.
  • The potential at some point r is V = keq/r.

Multiple Charges

  • The electric potential due to several point charges is the sum of the potentials due to each individual charge.
  • This is another example of the superposition principle.
  • The sum is the algebraic sum: V = ke Σ(qᵢ/rᵢ).
  • V = 0 at r = ∞.
  • For two charged particles, the potential energy of the system U = ke (q₁q₂ / r₁₂).
  • If two charges are the same sign, U is positive and work must be done to bring the charges together.
  • If the two charges have opposite signs, U is negative and work is done to keep the charges apart.
  • For a system with three charges, the total potential energy is U = ke (q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃).
  • The result is independent of the order of the charges.

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