# Magnetic Effects of Current and Magnetism

## 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 = μnI

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.
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