Molly Ayala
Electric potential, also known as electric field potential or potential drop, is the electric potential energy per unit of electric charge. It is the amount of work needed to move a test charge from a reference point to a specific point in a static electric field. The formula for electric potential is V = kQ/r, where V is the electric potential energy, k is Coulomb's constant, Q is the charge creating the electric potential, and r is the distance from the point charge to the charge creating the electric potential. The SI unit of electric potential is the volt (V), named after Alessandro Volta.
| Characteristics | Values |
|---|---|
| Definition | Electric potential energy per unit of electric charge |
| Formula | V = kQ/r |
| Unit | Volt (V) |
| Reference point | Zero units |
| Reference level | Infinity |
| Potential difference | V_B-V_A |
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What You'll Learn
Electric potential energy per unit charge
The electric potential at a point in an electric field, often referred to as electric potential energy per unit charge, can be calculated using the equation $V = \frac{kQ}{r}$, where $k$ is Coulomb's constant ($8.99 x 10^9 N m^2/C^2$), $Q$ is the charge creating the electric potential, and $r$ is the distance from the point to the charge. The SI unit of electric potential is the volt (V), in honour of Alessandro Volta, and the electric potential difference between two points in space is known as voltage.
The electric potential difference between two points $A$ and $B$, $V_B-V_A$, is the change in potential of a charge $q$ moved from $A$ to $B$. The general formula for the potential energy of a test charge $q$ at point $P$ relative to reference point $R$ is $U_p = - \int_R^p \vec{F} \cdot d\vec{l}$. When we substitute in the definition of the electric field ($\vec{E} = \vec{F}/q$), this becomes $U_p = -q \int_R^p \vec{E} \cdot d\vec{l}$. Applying our definition of potential ($V = U/q$) to this potential energy, we find that, in general, $V_p = - \int_R^p \vec{E} \cdot d\vec{l}$.
The electric potential energy of any given charge or system of charges is defined as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration. In an electrical circuit, the potential between two points is defined as the amount of work done by an external agent in moving a unit charge from one point to another.
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Electric potential difference
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is defined as electric potential energy per unit of electric charge. In other words, it is the amount of work needed to move a test charge from a reference point to a specific point in a static electric field. The reference point is usually the Earth or a point at infinity, though any point can be used. The electric potential at the reference point is defined as zero units.
The SI unit of electric potential is the volt (V), named after Alessandro Volta. The volt is also the unit of electric potential difference, or voltage, which is the difference in electric potential between two points in an electric field. Voltage describes the work done per unit charge when moving a charge between two points, and it serves as the driving force that causes electric charges to flow in an electrical circuit.
The electric potential at a point in an electric field, or electric potential energy per unit charge, is calculated using the equation:
> V = kQ/r
Where 'k' is Coulomb's constant (8.99 x 10^9 N m^2/C^2), 'Q' is the charge creating the electric potential, and 'r' is the distance from the point to the charge. This equation is similar to the equation for electric field but with distance to a single power rather than squared.
The general formula for the potential energy of a test charge 'q' at point 'P' relative to reference point 'R' is:
> Up = -q ∫_R^p E . dl
Substituting the definition of the electric field (E = F/q) into this equation and then applying our definition of potential (V = U/q) yields:
> Vp = - ∫_R^p E . dl
The electric potential energy of a test charge is:
> Up = qtVp = qtk∑(1^N) (qi/ri)
Where 'N' is the number of charges fixed in space, 'qi' is the test charge, and 'ri' is the distance from the test charge to each of the fixed charges.
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Electric potential at infinity
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is defined as electric potential energy per unit of electric charge. It is denoted by V or φ. The SI unit of electric potential is the volt, abbreviated as V, in honour of Alessandro Volta.
The formula for electric potential is:
> \[V_p = \sum_1^N k\dfrac{q_i}{r_i} = k\sum_1^N \dfrac{q_i}{r_i}.\]
Therefore, the electric potential energy of the test charge is:
> \[U_p = q_tV_p = q_tk\sum_1^N \dfrac{q_i}{r_i}.\]
The reference point for electric potential is typically assumed to be Earth or a point at infinity, and the electric potential at this reference point is zero. This is analogous to taking sea level as the reference point for gravitational potential energy. In electrodynamics, the electric potential at infinity is assumed to be zero.
However, it is important to note that when time-varying fields are present, the electric field cannot be expressed solely as a scalar potential. Instead, it is expressed as both the scalar electric potential and the magnetic vector potential, forming a four-vector.
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Electrostatic potential energy
Electric potential energy, also known as electrostatic potential energy, is the energy stored in a system of electric charges due to their positions and interactions. It is a scalar quantity with only magnitude and no direction. It is measured in units of joules (J) and can be calculated using a formula similar to Coulomb's Law: k(q1q2)/r, where k is the Coulomb's law constant, q1 and q2 are the two interacting charges, and r is the distance between them.
The electric potential at a point in an electric field, or electric potential energy per unit charge, can be calculated using the equation V = kQ/r, where 'k' is Coulomb's constant (8.99 x 10^9 N m^2/C^2), 'Q' is the charge creating the electric potential, and 'r' is the distance from the point to the charge.
The electric potential at infinity is assumed to be zero, and the reference level used to define electric potential at a point is infinity, indicating that the force on a test charge is zero at the reference level. The surface of the Earth is often taken to be at zero potential since the addition or removal of charge from it will not alter its electrical state.
In an electrical circuit, the potential between two points (E) is defined as the amount of work done (W) by an external agent in moving a unit charge (Q) from one point to another. This is also known as the electric potential difference or voltage, which is the difference in electric potential between two points in an electric field.
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Electric potential in an electric circuit
Electric potential, also known as electric field potential, potential drop, or electrostatic potential, is a fundamental concept in understanding the behaviour of electric circuits. It refers to the amount of work required to move a test charge from a reference point to a specific point in a static electric field. This can be understood as the electric potential energy per unit of electric charge. The formula for electric potential in a simple case with a point charge is:
> V_p = k * (q_i / r_i)
Where V_p is the electric potential, q_i is the charge, r_i is the distance from the charge, and k is a constant.
In an electric circuit, electric potential is crucial in understanding the behaviour of electrons and the flow of current. A circuit typically consists of a battery and a resistor, forming two nodes: one where the positive battery terminal connects to the resistor, and the other where the negative battery terminal is connected. The electric potential at these nodes is the potential difference between them, often measured in volts (V). This potential difference indicates the work done per unit charge to move a charge between the nodes.
When considering more complex circuits with multiple nodes, a reference node (often ground) is chosen. The voltage at any other node is then understood as the potential difference between that node and the reference node. This is measured using a voltmeter, which compares the measured potential with the reference potential. It's important to note that absolute values of potential cannot be measured; only potential differences are measurable.
The concept of electric potential is closely related to the electric field. While the electric field describes the force exerted on a positive test charge at a given point, the electric potential represents the work required to move that charge between points in the field. This relationship allows for a more convenient calculation of the work done on a charge, as the magnitude of the charge is not required.
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Frequently asked questions
The formula for electric potential is V = kQ/r, where V is the electric potential, k is Coulomb's constant (8.99 x 10^9 N m^2/C^2), Q is the charge creating the electric potential, and r is the distance from the point to the charge.
The SI unit of electric potential is the volt (V), which is why the electric potential difference between two points in space is known as voltage.
Electric potential energy is the energy stored in a system of electric charges due to their positions and interactions. It is a scalar quantity and is measured in joules.
Electric potential is a measure of the electric potential energy per unit charge at a specific location within an electric field. It represents the amount of work done per unit charge to bring a test charge from infinity to a specific point in an electric field.
Voltage, also known as electric potential difference, represents the difference in electric potential between two points in an electric field. It describes the work done per unit charge when moving a charge between two points and serves as the driving force for electric charge flow in a circuit.
