# Magnetic Force

**Magnetic Force:**

The magnetic force between two moving charges may be described as the effect exerted upon either charge by a magnetic field created by the other.

Magnetic force is a consequence of electromagnetic force and is caused due to the motion of charges. We have learned that a moving charge surrounds itself with a magnetic field.

Magnetic force is a force that acts on charged particles or objects moving through a magnetic field. It is one of the four fundamental forces of nature.

The magnetic force is proportional to the charge of the particle, the strength of the magnetic field, and the velocity of the particle perpendicular to the magnetic field. It is also perpendicular to both the direction of the particle's velocity and the direction of the magnetic field.

**The force can be calculated using the following formula:**

F = quBsinθ

where

· F is the magnetic force (in Newtons, N)

· q is the charge of the particle (in Coulombs, C)

· u is the velocity of the particle (in meters per second, m/s)

· B is the strength of the magnetic field (in Tesla, T)

· θ is the angle between the direction of the particle's velocity and the direction of the magnetic field

**Magnetic Force on a Current-Carrying Conductor**

Let us discuss the force due to the magnetic field in a straight current-carrying rod.

A rod of uniform length l and cross-sectional area A. let the number density of mobile electrons be given by n.

Then the total number of charge carriers can be given by nAI,

where I is the steady current in the rod.

The drift velocity of each mobile carrier is assumed to be given as vd.

When the conducting rod is placed in an external magnetic field of magnitude B, the force applied on the mobile charges or the electrons can be given as:

**F= (nAI) qvd×B**