# Behavior of a Charge in Magnetic field

## Introduction

This is one of the important topics in AP Physics C E&M.

Charge feels force on it. The force is dependent on the charge (q), velocity(v)and magnetic field (B).

Let us consider this particle has a charge q and it moves in the direction of magnetic field B (motion in a magnetic field); the velocity is v and θ is the angle between B and V

We have different cases for a force experienced by a charge

### CASE 1: if θ = 0 or 180

Velocity of charge is parallel or anti-parallel to magnetic field.

F= 0.

Trajectory = straight line.

### CASE 2: if θ = 90

Velocity of charge is perpendicular to magnetic field

F = F centripetal

Trajectory = circle (right-hand thumb rule )

## Biot savart law

Biot savart law is a fundamental relationship between an electric current I and the magnetic field B in physics.

Biot savart law equations describe the relationship between the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and electric current.

dL = infinitesimal length of a conductor carrying electric current.

## Magnetic Field

Magnetic Field is a region of space near a magnet.

In other words

A magnetic field is a field that describes the magnetic influence on moving electric charges and electric currents. A moving charge(q) in a magnetic field experiences a force perpendicular to its own velocity (v) and to the magnetic field. It can be denoted with B.

The electric field produced by a point charge q at rest at the origin is

Where F is Electrostatics Force, and q is point charge.

Magnetic field lines

The magnetic field lines are a visual and intuitive realisation of the magnetic field.

## The Dipole in a uniform magnetic field

The magnetic field lines give us an

approximate idea of the magnetic field (B). To

determine the magnitude of B accurately. This is done by placing a small compass needle of known magnetic moment (m) and moment of inertia (I)

and allowing it to oscillate in the magnetic field.

The torque on the needle is

In magnitude

Here τ is restoring torque and θ is the angle between m and B.

To know more about the other chapters tested in AP Physics C E&M, Check out Succeeding in AP Physics C Electricity and Magnetism