Umair Gaines
The electric force between two charged particles is calculated using Coulomb's law, which states that the magnitude of the force is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. The force is attractive or repulsive, depending on the signs of the charges. The electric field, a concept proposed by Michael Faraday, is a vector field that can be associated with each point in space, and it is defined as the force per unit charge exerted on a positive test charge at rest at that point. The direction of the electric field is determined by the sign of the charge. The Lorentz force law, on the other hand, describes the combination of electric and magnetic force on a point charge due to electromagnetic fields.
| Characteristics | Values |
|---|---|
| Definition | The total electric force is the magnitude of the attractive or repulsive electrostatic force between two point charges |
| Formula | F = ke x q1 x q2/ r^2 |
| Variables | F = force, ke = 8.988E9 (N x m2)/C2, q1 and q2 = charges of particles in coulombs, r = distance between particles |
| Direction | The direction of the electric field is determined by the sign of the charge |
| Positive Charges | Force is radially outward |
| Negative Charges | Force is radially inward |
| Same Charges | Particles repel each other |
| Opposite Charges | Particles attract each other |
| Inverse Square Law | The force is inversely proportional to the square of the distance between the charges |
| Direct Proportionality | The magnitude of the force is directly proportional to the product of the magnitudes of the charges |
| Superposition Principle | The resulting field is the vector sum of the fields generated by each particle |
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What You'll Learn
Electric field
The concept of an electric field was proposed by 19th-century English physicist Michael Faraday. An electric field is an electric property associated with each point in space where a charge is present. It is a vector field that can be understood as the force per unit charge exerted on a positive test charge at rest at that point. The electric field is radially outwards from a positive charge and radially inwards towards a negative point charge. The direction of the electric field is determined by the sign of the charge.
The magnitude and direction of an electric field can be determined by the Coulomb force on the test charge. Coulomb's law, or Coulomb's inverse-square law, calculates the amount of force between two electrically charged particles at rest. The law states that the magnitude of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. The force acts along the shortest line joining the charges and is repulsive if the charges have the same sign and attractive if they have different signs.
The electric field can also be found using Gauss's law, which states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric field at a point due to a point charge can be given by the equation:
\[\vec E = \frac{\vec F}{Q}\]
Where:
- \(\vec{E}\) is the electric field
- \(\vec{F}\) is the force
- \(Q\) is the charge
The electric field is a fundamental concept in physics, similar to gravitational fields, and is useful for understanding the behaviour of charged particles and the forces they experience.
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Coulomb's Law
Mathematically, Coulomb's Law can be expressed as:
> F = ke × q1 × q2/r²
Where F is the force between the charges, ke is the electrostatic constant (approximately 8.988 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
The direction of the force between the charges depends on the signs of the charges. If the charges have the same sign, the force is repulsive, and the charges push each other away. If the charges have opposite signs, the force is attractive, and the charges pull each other closer.
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Gauss's Law
Mathematically, Gauss's Law can be expressed in integral and differential forms using vector calculus, with both forms being equivalent due to their relationship through the divergence theorem (also known as Gauss's theorem). The law can be stated in terms of the electric field (E) or the electric displacement field (D) and the corresponding charge.
The electric flux ΦE through a closed surface S enclosing any volume V is given by the equation:
ΦE = Q / ε0
Where:
- ΦE is the electric flux through the closed surface.
- Q is the total charge enclosed within volume V.
- Ε0 is the electric constant.
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Lorentz force
The Lorentz force law, or equation, describes the force acting on a moving point charge in the presence of electromagnetic fields. It is represented by the formula F = q(E + v × B), where F is the total electromagnetic force, q is the charge, E is the electric field, v is the velocity, and B is the magnetic field. The first term, qE, represents the electric force, while the second term, q(v × B), represents the magnetic force. The direction of the Lorentz force is given by the right-hand rule, which helps determine the direction of the magnetic part of the force.
The Lorentz force has important applications in understanding the behaviour of charged particles in electromagnetic fields. For example, it explains the motion of a charged particle in a uniform magnetic field. If the velocity (v) is perpendicular to the magnetic field (B), the particle will follow a circular trajectory. If the angle between v and B is less than 90 degrees, the particle orbit will be a helix. Lorentz force is also used in cathode ray tube televisions to deviate electrons so that they land on specific spots on the screen.
The Lorentz force law was first derived by Hendrik Lorentz in 1895. However, the concept of electric and magnetic fields that underpin the Lorentz force originated with the theories of Michael Faraday, particularly his idea of 'lines of force'. J.J. Thomson played a significant role in verifying the Lorentz force law through his experiments with cathode rays in 1881 and 1897. These experiments demonstrated that cathode rays were indeed streams of charged particles, as predicted by the Lorentz force equation.
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Weber force
The Weber force is a central force that complies with Newton's third law, demonstrating the conservation of momentum, energy, and angular momentum. It is a theory of electromagnetism that was proposed by Wilhelm Eduard Weber and preceded Maxwell's electrodynamics. Weber electrodynamics is based on the contributions of André-Marie Ampère, Carl Friedrich Gauss, and Weber himself.
Weber's theory interprets the force of a current on a test charge by assuming that a current-carrying conductor contains negative and positive point charges that move at slightly different relative velocities. This results in slight deformations of the force, leading to residual forces that correspond to the Lorentz force. The Lorentz force is a force exerted by the electromagnetic field on a charged particle, and it is defined by the vector fields E (electric field) and B (magnetic field).
Weber electrodynamics is only applicable under certain conditions, such as electrostatics, magnetostatics, and quasistatic approximations. It is not suitable for describing electromagnetic waves or calculating forces between rapidly moving or significantly accelerated charged particles. However, it offers a unique advantage by allowing the description of magnetic forces between direct currents, low-frequency alternating currents, and permanent magnets without relying on a magnetic field.
In terms of Faraday's law, the Weber (symbolized as Wb) is the SI unit of magnetic flux. It is defined as the magnetic flux that, when linking a circuit of one turn, produces an electromotive force of one volt if reduced to zero at a uniform rate in one second. One Weber is also equivalent to the total magnetic flux across a surface of one square meter perpendicular to a magnetic flux density of one tesla. The Weber unit is derived from Faraday's law of induction, with a relationship of 1 Wb = 1 V·s (volt-second).
The Weber unit is named after German physicist Wilhelm Eduard Weber, and it plays a crucial role in understanding magnetic fields and their interactions with charged particles.
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Frequently asked questions
The total electric force is calculated using Coulomb's law. This states that the magnitude of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them.
The formula for total electric force is: F = ke x q1 x q2/r^2. Where F is the force, q1 and q2 are the charges, r is the distance between the charges, and ke is the constant 8.988E9 (N x m^2)/C^2.
The Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. The total electric force, or Coulomb force, is the electrostatic force between two charges.
