Otis Singleton
Electric fields are important in many areas of physics and are fundamental to electrical technology. They are physical fields that surround electrically charged particles, such as electrons, and describe their capacity to exert attractive or repulsive forces on other charged objects. The electric field is defined as a vector field that associates a force per unit of charge exerted on a small test charge at each point in space. The SI unit for the electric field is the volt per meter (V/m). Electric fields can be derived from the electric potential, which is the negative of the gradient of the electric potential, given by E = −grad V. This derivative relationship is with respect to position, and the electric field can be calculated at a given point using vector calculus. Understanding the derivative of electric force is crucial for comprehending the behaviour of charged particles and their interactions in various contexts, including atomic physics and chemistry.
| Characteristics | Values |
|---|---|
| Definition | A physical field that surrounds electrically charged particles such as electrons |
| Formula | E = −grad V |
| Direction | The direction in which the potential decreases most rapidly, moving away from the point |
| Magnitude | The change in potential across a small distance in the indicated direction divided by that distance |
| SI Unit | Volt per meter (V/m) or newton per coulomb (N/C) |
| Relationship with Magnetic Fields | In the absence of a time-varying magnetic field, the electric field is conservative (curl-free) |
| Relationship with Potential Energy | The electric field is the negative gradient of the potential energy |
| Relationship with Force | The electric field is the electric force per unit charge |
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What You'll Learn
- Electric fields are caused by electric charges
- The electric field is the negative of the gradient of electric potential
- The electric field is a vector field
- The electric field is the force per unit of charge exerted on a test charge
- Faraday's law and the relationship between a time-varying magnetic field and the electric field
Electric fields are caused by electric charges
The strength of the electric field is determined by the magnitude of the charges and the distance between them. According to Coulomb's law, the greater the magnitude of the charges, the stronger the force, and the greater the distance between the charges, the weaker the force. The electric field can be visualized using the concept of 'lines of force', introduced by Michael Faraday, where the direction of the field at each point is indicated by the direction of the lines.
The electric field is defined as a vector field, which means it has both magnitude and direction. At each point in space, the electric field is defined as the force experienced by an infinitesimally small stationary test charge at that point, divided by the charge. The SI unit for the electric field is the volt per meter (V/m), equivalent to the newton per coulomb (N/C).
The study of electric fields created by stationary charges is called electrostatics. Faraday's law describes the relationship between a time-varying magnetic field and the electric field. It states that the curl of the electric field is equal to the negative time derivative of the magnetic field. This results in two types of electric fields: electrostatic fields and fields arising from time-varying magnetic fields.
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The electric field is the negative of the gradient of electric potential
The electric field is a physical field that surrounds electrically charged particles, such as electrons. It describes the capacity of a single charge or group of charges to exert attractive or repulsive forces on another charged object. The electric field is defined as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal test charge at rest at that point. The SI unit for the electric field is the volt per meter (V/m), which is equal to the newton per coulomb (N/C).
The electric field can be derived from the electric potential. In vector calculus notation, the electric field is given by the negative of the gradient of the electric potential, E = −grad V. This expression specifies how the electric field is calculated at a given point. The direction of the electric field is the direction in which the potential decreases most rapidly, moving away from the point. The magnitude of the field is the change in potential across a small distance in the indicated direction divided by that distance.
The gradient of the potential is like the steepness of a mountain. We think of the gradient as being in the direction where the elevation of the mountain increases, but we have to add a minus sign because things roll down the mountain and not up. So, the electric force points in the direction of decreasing potential because things fall down, not up.
The negative sign is also related to the work done by the field. When an external force is applied to move a charge in an electric field, work is done, and energy is given to the system. However, since only the position of the charge has changed, the energy must be stored in the field. The work done by the field must be negative because it acts in the opposite direction of the external force, and the force applied by the field is equal and opposite to the external force.
The electric field is a function of the force on a +1C charge placed at a point in the field. The electric potential is a function such that the gradient at a point is equal to the electric field at that point.
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The electric field is a vector field
The electric field at a point in space is defined as the force per unit of charge that would act on an infinitesimally small stationary test charge placed at that point. This force is a vector quantity, meaning it has both magnitude and direction. The electric field, therefore, can be described as a vector field. Each point in the electric field has a specific direction and magnitude, which can be visualised using lines of force or field lines. These lines indicate the direction of the electric field and are denser closer to the central charge, where the field is strongest.
The electric field is associated with the concept of potential or voltage. The difference in electric potential between two points in space is called the potential difference or voltage. The electric field can be derived from the electric potential, and in vector calculus, it is given by the negative gradient of the electric potential. This relationship is expressed as E = −grad V, where E represents the electric field and V represents the electric potential.
The electric field is also related to the magnetic field, as described by Faraday's law. According to Faraday's law, the curl of the electric field is equal to the negative time derivative of the magnetic field. This implies that there are two types of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. In the absence of time-varying magnetic fields, the electric field is considered conservative or curl-free.
The electric field is essential in understanding the behaviour of charged particles. Charged particles interact with each other through electric fields, exerting attractive or repulsive forces depending on the charges involved. Coulomb's law describes these forces, stating that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
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The electric field is the force per unit of charge exerted on a test charge
An electric field, or E-field, is a physical field that surrounds electrically charged particles, such as electrons. It describes the capacity of a single charge or group of charges to exert attractive or repulsive forces on another charged object. This force is experienced per unit of charge exerted on an infinitesimally small test charge.
The electric field is defined as a vector field that associates each point in space with the force per unit of charge exerted on a test charge at rest at that point. The SI unit for the electric field is the volt per meter (V/m), equal to the newton per coulomb (N/C). The electric field at each point in space is defined as the force experienced by an infinitesimally small stationary test charge at that point, divided by the charge.
The electric field can be derived from the electric potential, which describes the force on a charge. In vector calculus notation, the electric field is given by the negative of the gradient of the electric potential, E = −grad V. This expression specifies how the electric field is calculated at a given point. Since the field is a vector, it has both a direction and magnitude. The direction is that in which the potential decreases most rapidly, moving away from the point. The magnitude of the field is the change in potential across a small distance in the indicated direction, divided by that distance.
The relationship between the electric field and its potential involves a derivative with respect to position. In one dimension, the electric field (E) of a charge (Q) is the negative derivative of its potential (V). The electric field is the negative of the gradient of the potential energy, indicating that particles are attracted towards lower potential energy. This is why electric forces tend to drive positive charges from higher to lower potential.
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Faraday's law and the relationship between a time-varying magnetic field and the electric field
Electric fields are important in many areas of physics and are fundamental to electrical technology. They are physical fields that surround electrically charged particles, such as electrons, and describe their capacity to exert attractive or repulsive forces on other charged objects.
Faraday's law of induction describes the relationship between a time-varying magnetic field and the electric field. It states that a changing magnetic field can induce an electric field and, conversely, that a moving electric field can produce a magnetic field. This discovery was made by Michael Faraday in 1831, with similar observations made by Joseph Henry in 1832. Faraday demonstrated that when a bar magnet was rapidly moved into or out of a coil of wire, transient currents were observed.
Faraday's law can be expressed mathematically as:
> \(\varepsilon = - \frac { \partial \Phi _ { \mathrm { B } } } { \partial \mathrm { t } }\).
Here, \(\varepsilon\) represents the induced electromotive force (EMF) and \(\frac { d \Phi _ { \mathrm{B} } } {\mathrm{ d t} }\) represents the rate of change of magnetic flux with time.
The Maxwell-Faraday equation, a set of equations formulated by James Clerk Maxwell, describes how a time-varying magnetic field induces an electric field and drives a current around a loop. This phenomenon is the basis for the operation of electrical machines such as synchronous generators.
The study of magnetic and electric fields that change over time is called electrodynamics, and it highlights the interconnected nature of electric and magnetic forces, now considered manifestations of the same underlying force.
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Frequently asked questions
An electric field, sometimes called an E-field, is a physical field that surrounds electrically charged particles, such as electrons. It describes the capacity of a single charge or group of charges to exert attractive or repulsive forces on another charged object.
The electric field is the negative of the potential derivative with respect to displacement. The electric field is given by the negative of the gradient of the electric potential, E = −grad V.
The electric field is just the electric force per unit charge. The electric field behaves similarly to force because it is attracted towards lower potential energy.
Faraday's law describes the relationship between a time-varying magnetic field and the electric field. It states that the curl of the electric field is equal to the negative time derivative of the magnetic field. This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields.
