Electric Fields: Definition and Field Lines

Electromagnetic fields are areas in space where electromagnetic forces are present.
These forces are mediated by photons and encompass both electric and magnetic fields.

Electric fields are regions around electrically charged objects where other charged objects experience a force.
Electric field strength (E) is defined as the force per unit positive charge exerted on a test charge placed in the field (E = F/q).
Electric fields are vector fields, having both magnitude and direction.
The direction of the electric field is the direction of the force on a positive test charge.

Electric field lines are used to visualize electric fields.
They indicate the direction of the electric field at any point.
Field lines originate from positive charges and terminate on negative charges.
The density of field lines indicates the strength of the electric field (more lines, stronger field).
Field lines never cross each other.

Electric potential (V) at a point is the electric potential energy per unit charge at that point.
It is a scalar quantity, measured in volts (V).
Potential difference (ΔV) between two points is the work done per unit charge to move a charge between those points.
Equipotential surfaces are surfaces where the electric potential is constant.
Electric field lines are always perpendicular to equipotential surfaces.
The electric field is related to the negative gradient of the electric potential (E = -dV/dr).

The electric field due to a single point charge (Q) at a distance (r) is given by Coulomb's law: E = kQ/r², where k is Coulomb's constant.
For multiple point charges, the net electric field at a point is the vector sum of the electric fields due to each charge individually (superposition principle).

The electric potential due to a single point charge Q at a distance r is given by: V = kQ/r.
For multiple point charges, the net electric potential at a point is the scalar sum of the electric potentials due to each charge individually.

A charged particle in an electric field experiences a force: F = qE.
If the electric field is uniform, the particle experiences a constant force, resulting in constant acceleration (like projectile motion).
The work done by the electric field on a charged particle is equal to the change in its kinetic energy.
The electric potential energy of a charged particle in an electric field changes as it moves, related to the work done.

Magnetic fields are regions of space where magnetic forces are exerted.
These forces are exerted on moving electric charges and magnetic materials.
Magnetic fields are vector fields, having both magnitude and direction.
Magnetic fields are created by moving electric charges (electric currents) and intrinsic magnetic moments of elementary particles.
Magnetic field lines are used to visualize magnetic fields.
They indicate the direction of the magnetic field at any point.
Magnetic field lines form closed loops; they do not start or end at a point (magnetic monopoles have not been observed).
The density of field lines indicates the strength of the magnetic field (more lines, stronger field).

A charge q moving with velocity v in a magnetic field B experiences a force: F = q(v x B).
The magnitude of the force is F = qvBsinθ, where θ is the angle between v and B.
The direction of the force is perpendicular to both v and B, given by the right-hand rule.
If the charge's velocity is parallel to the magnetic field, it experiences no magnetic force.
If the charge is stationary, it also experiences no magnetic force.

A wire carrying a current I in a magnetic field B experiences a force: F = I(L x B), where L is a vector representing the length and direction of the wire segment in the field.
The magnitude of the force is F = ILBsinθ, where θ is the angle between L and B.
The direction of the force is perpendicular to both L and B, given by the right-hand rule.

A current-carrying wire produces a magnetic field around it.
The shape and strength of the magnetic field depend on the geometry of the wire.

The magnetic field at a distance r from a long straight wire carrying a current I is given by: B = (μ₀I)/(2πr), where μ₀ is the permeability of free space.
The magnetic field lines are concentric circles around the wire.
The direction of the magnetic field is given by the right-hand grip rule (thumb points in the direction of the current, fingers curl in the direction of the magnetic field).

A solenoid is a coil of wire wound into a tightly packed helix.
The magnetic field inside a long solenoid is approximately uniform and parallel to the axis of the solenoid: B = μ₀nI, where n is the number of turns per unit length (n = N/L).
The magnetic field outside the solenoid is weak.

The magnetic field at the center of a circular loop of radius R carrying a current I is given by: B = (μ₀I)/(2R). The field lines go through center of loop, perpendicular to the loop.

A charged particle moving in a uniform magnetic field experiences a force perpendicular to its velocity, causing it to move in a circular path.
The magnetic force provides the centripetal force required for circular motion: qvB = mv²/r.
The radius of the circular path is given by: r = (mv)/(qB).
The period of the circular motion is given by: T = (2πm)/(qB).
If the charged particle has a velocity component parallel to the magnetic field, it will move in a helical path.
Magnetic fields do no work on moving charges because the magnetic force is always perpendicular to the velocity. Kinetic energy remains constant, but velocity direction changes.

Mass spectrometers use magnetic fields to separate ions based on their mass-to-charge ratio.
Velocity selectors use crossed electric and magnetic fields to select particles with a specific velocity.
Electric motors use the force on current-carrying wires in magnetic fields to produce rotational motion.
Magnetic confinement is used in fusion reactors to contain plasma using magnetic fields.