Table of Contents

Toggle## 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 = μ_{₀}nI

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.