Gravitational, Electric, and Magnetic Fields

Posted on Mar 1, 2025 in Physics

Here’s a comparison of gravitational, electric, and magnetic fields:

Field Characteristics

  • Gravitational Field:
    • A field of forces acting on bodies with mass.
    • The force exerted is proportional to the mass acted upon.
    • The gravitational force is always attractive.
    • The field is defined at each point by the vector field g = F / m.
    • The gravitational field strength due to a point mass is inversely proportional to the square of the distance: g = G · m/r2.
    • The universal gravitational constant (G) is the same in all media.
    • It is a conservative force field.
    • The work required to move a mass between two points in the field is independent of the trajectory.
    • A gravitational potential (U) can be defined at each point in the field.
    • The gravitational potential (V) at a point is the gravitational potential energy (Ep) per unit mass: V = Ep / m.
    • The gravitational potential at a point due to a point mass is inversely proportional to the distance: V = –Gm / r.
  • Electric Field:
    • A field of forces acting on bodies with electric charges.
    • The force exerted is proportional to the electric charge.
    • The electric force can be attractive or repulsive.
    • The field is defined at each point by the vector field strength E = F / q.
    • The intensity of the electric field due to a point charge is inversely proportional to the square of the distance: E = K · q/r2.
    • The electrostatic constant (K) has a different value for different media.
    • It is a conservative force field.
    • The work required to move a charge between two points in the field is independent of the trajectory.
    • An electric potential (V) can be defined at each point in the field.
    • The electric potential (V) at a point is the electric potential energy of a unit positive electric charge: Ep = qV.
  • Magnetic Field:
    • A force field that acts on moving electric charges.
    • The force exerted is proportional to the electric charge.
    • The magnetic force can be attractive or repulsive.
    • The field is defined at each point by the magnetic induction vector B: F = q (v × B).
    • The magnetic field due to a conductive element through which current flows is inversely proportional to the square of the distance: ΔB = (μ0I/4π) · (Δl × ur / r2).
    • The magnetic permeability (μ) has a different value for different media.
    • It is a non-conservative force field. A potential function that depends only on the position of bodies in the magnetic field cannot be defined.
    • The work required to move a charge between two points in the field depends on the trajectory.
    • A magnetic potential cannot be defined at each point in the field.

Action of Magnetic Field on Moving Electric Charges

TypeCalculationRepresentationApplications
Magnetic Force on a moving charge (Lorentz Force)Particle accelerator, Mass Spectrometer
Magnetic force on a current element (straight wire)Galvanometer: measuring current intensity
Forces between currentsAmpere (Ah): Two straight parallel conductors in a vacuum at a distance of one meter are traversed in the same direction. If a force of 2 × 10-7 N/m is measured, the current flowing through is one ampere.

Coulomb’s Law

Coulomb’s Law states that the force established between point electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them: F1,2 = [K (Q1Q2) / r2] u

Features:

  1. The direction of the force coincides with that of the straight line joining the charges.
  2. The force may be attractive or repulsive, depending on the sign of the charges.
  3. These are distance forces, which are manifested even in a vacuum.
  4. It verifies the principle of action-reaction.
  5. It verifies the principle of superposition.
  6. It’s a central force: the direction of all force vectors converge at the same spot, and the magnitude depends on the distance to it.
  7. It is a conservative force: the work done by the electric forces is equal to the change in potential energy.

Study of Electric Field

A charged body creates a disturbance in the area surrounding it, resulting in a central and conservative field.

Particle Accelerator

A device in which charged particles are accelerated to high kinetic energy. The collision of these particles with atomic nuclei or other particles produces nuclear reactions that allow us to study the composition of matter. In a cyclotron, Fmagnetic = Fcentripetal.

Vmax = (q · B · R) / m

R = (m · v) / (q · B)

T = 2πR / v

Mass Spectrometer

A device that uses a magnetic field to measure the masses of different isotopes of the same chemical element.