# Lorentz Force, About Lorentz Force, Formula of Lorentz Force (For CBSE, ICSE, IAS, NET, NRA 2022)

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• The Lorentz Force is the Force on a Charged Particle Due to Electric and Magnetic Fields.
• A Charged Particle in an Electric Field Will Always Feel a Force Due to this Field.
• Hendrik Antoon Lorentz was a Dutch physicist who explained the theories related to electromagnetic radiation. He mainly concentrated on the relationship between magnetism, light, and electricity.
• A Charged Particle in a Magnetic Field Will Only Feel a Force Due to the Magnetic Field if It is Moving Relative to this Field.
• These Two Effects Are Often Studied Separately, but the Sum of These Two Effects Creates a Force That We Call the Lorentz Force.
• In the Year 1895, Hendrik Lorentz Derived the Modern Formula of Lorentz Force.

• It is defined as the combination of the magnetic and electric force on a point charge due to electromagnetic fields.
• It is used in electromagnetism and is also known as the electromagnetic force.

## Formula of Lorentz Force

Formula for the charged particle is as follows

Where,

• F is the force acting on the particle
• q is the electric charge of the particle
• v is the velocity
• E is the external electric field
• B is the magnetic field

Formula for continuous charge distribution is as follows:

Where,

• dF is a force on a small piece of the charge
• dq is the charge of a small piece
• When a small piece of charge distribution is divided by the volume dV, following is the formula:

Where,

• f is the force per unit volume
• ρ is the charge density

## Importance of Lorentz Force

• It explains the mathematical equations along with physical importance of forces acting on the charged particles that are travelling through the space containing electric as well as magnetic field.
• This is the importance of the Lorentz force.

## Right-Hand Rule

• The right-hand rule is useful to find the magnetic force as it becomes easy to visualize the direction as given in Lorentz force law.
• It is understood that magnetic force is perpendicular to both the magnetic field and charge velocity.

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