Magnetic Force on a Moving Charge:
F = q(v × B)
where F is the magnetic force on the charge,
- q is the charge of the particle,
- v is the velocity of the particle, and
- B is the magnetic field.
Magnetic Force on a Current-Carrying Conductor:
F = IL × B
where F is the magnetic force on the conductor,
- I is the current flowing through the conductor,
- L is the length of the conductor in the magnetic field, and
- B is the magnetic field.
Motion of a Charged Particle in a Magnetic Field:
F = q(v × B)
F = ma
Where F is the magnetic force on the charged particle,
- q is the charge of the particle,
- v is the velocity of the particle,
- B is the magnetic field,
- m is the mass of the particle, and
- a is the acceleration of the particle.
Magnetic Field due to a Straight Current-Carrying Conductor:
B = μ_₀I\over 2πr
where B is the magnetic field at a point due to the conductor,
- μ₀ is the permeability of free space,
- I is the current flowing through the conductor, and
- r is the distance from the conductor.
Magnetic Field Inside a Solenoid:
B = μ₀nI
where B is the magnetic field inside the solenoid,
- μ₀ is the permeability of free space,
- n is the number of turns per unit length, and
- I is the current flowing through the solenoid.
Force and Torque on a Current Loop:
F = I(a × B)
τ = NIABsinθ
Where F is the magnetic force on the loop,
- I is the current flowing through the loop,
- a is the area vector of the loop,
- B is the magnetic field,
- N is the number of turns in the loop,
- A is the area of the loop, and
- θ is the angle between the normal to the plane of the loop and the magnetic field.
Electromagnetic Induction:
ε = – dΦ\over dt
where ε is the induced emf,
- d(Φ) is the change in magnetic flux,
- dt is the time interval.
Faraday’s Law and Lenz’s Law:
ε = – dΦ\over dt
ε = Blv
where ε is the induced emf,
- d(Φ) is the change in magnetic flux,
- dt is the time interval,
- B is the magnetic field,
- l is the length of the conductor, and
- v is the velocity of the conductor.
