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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?
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?
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?
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?
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?
A system consists of a negative charge and an electric field. When does the system gain potential energy?
A system consists of a negative charge and an electric field. When does the system gain potential energy?
For a negative charge to move in the direction of the electric field, what must occur?
For a negative charge to move in the direction of the electric field, what must occur?
When a test charge is placed in an electric field, it experiences a force. What is the nature of this force?
When a test charge is placed in an electric field, it experiences a force. What is the nature of this force?
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?
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?
What does the infinitesimal displacement vector, $d\vec{s}$, represent in the context of electric potential energy?
What does the infinitesimal displacement vector, $d\vec{s}$, represent in the context of electric potential energy?
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?
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?
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?
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?
Why is the line integral used to calculate the work done by a conservative force independent of the path taken by the charge?
Why is the line integral used to calculate the work done by a conservative force independent of the path taken by the charge?
The electric potential is defined as the potential energy per unit charge. Which statement accurately describes the nature of electric potential?
The electric potential is defined as the potential energy per unit charge. Which statement accurately describes the nature of electric potential?
Which of the following is NOT true about electric potential?
Which of the following is NOT true about electric potential?
How will a charged particle behave when it moves in an electric field?
How will a charged particle behave when it moves in an electric field?
What is the important quantity associated with electric potential?
What is the important quantity associated with electric potential?
In practical applications involving electric potential, what is often assumed about the value of the potential at a convenient point in the field?
In practical applications involving electric potential, what is often assumed about the value of the potential at a convenient point in the field?
What characteristic defines electric potential in relation to charges that may be placed in the field?
What characteristic defines electric potential in relation to charges that may be placed in the field?
If a charge moves in an electric field without any change in its kinetic energy, what equation expresses the work performed on the charge?
If a charge moves in an electric field without any change in its kinetic energy, what equation expresses the work performed on the charge?
What is the definition of a volt (V) in terms of other SI units?
What is the definition of a volt (V) in terms of other SI units?
What amount of work is required to move a 1-coulomb charge through a potential difference of 1 volt?
What amount of work is required to move a 1-coulomb charge through a potential difference of 1 volt?
In atomic and nuclear physics, what unit of energy is commonly used in addition to the joule?
In atomic and nuclear physics, what unit of energy is commonly used in addition to the joule?
How is one electron-volt defined?
How is one electron-volt defined?
What is the energy equivalent of 1 eV in joules?
What is the energy equivalent of 1 eV in joules?
If a positive charge is released from rest in a uniform electric field, in which direction does it move?
If a positive charge is released from rest in a uniform electric field, in which direction does it move?
When a positive charge moves in the direction of the electric field, what is the sign of the change in potential?
When a positive charge moves in the direction of the electric field, what is the sign of the change in potential?
How are the force and acceleration related to the direction of the electric field for a positive charge placed within it?
How are the force and acceleration related to the direction of the electric field for a positive charge placed within it?
What principle can be used to determine the speed of a charged particle in a uniform electric field?
What principle can be used to determine the speed of a charged particle in a uniform electric field?
If the electric field is uniform, how can the equations for electric potential be simplified?
If the electric field is uniform, how can the equations for electric potential be simplified?
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?
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?
What is the relationship between electric field lines and electric potential?
What is the relationship between electric field lines and electric potential?
What type of field is produced around a positive point charge?
What type of field is produced around a positive point charge?
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?
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?
In the context of electric potential due to a point charge, what is the customary reference point for zero potential?
In the context of electric potential due to a point charge, what is the customary reference point for zero potential?
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?
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?
How is the electric potential due to several point charges determined?
How is the electric potential due to several point charges determined?
In calculating the electric potential due to multiple charges, what principle is applied?
In calculating the electric potential due to multiple charges, what principle is applied?
In the context of electric potential with multiple charges, what type of sum is used to calculate the total potential?
In the context of electric potential with multiple charges, what type of sum is used to calculate the total potential?
What is the electric potential at $r = \infty$?
What is the electric potential at $r = \infty$?
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?
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?
Under what circumstance is the potential energy U negative?
Under what circumstance is the potential energy U negative?
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?
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?
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?
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?
Flashcards
Electric potential and field direction
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
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
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
System gains potential energy
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Test charge in electric field
Test charge in electric field
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Work and external agent
Work and external agent
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Electric force is conservative
Electric force is conservative
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Electric Potential Definition
Electric Potential Definition
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Electric Potential Type
Electric Potential Type
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Scalar characteristic of electric field
Scalar characteristic of electric field
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What is a Volt
What is a Volt
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Electron-Volt
Electron-Volt
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Uniform field, positive charge
Uniform field, positive charge
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Electric field direction
Electric field direction
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Field of postive charge
Field of postive charge
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Electric potential
Electric potential
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Potential from multiple charges
Potential from multiple charges
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Charges with the same sign
Charges with the same sign
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Find the Total Potential Energy
Find the Total Potential Energy
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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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