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

$$

F=q(v \times B)

$$

$$

\mathrm{F}=\mathrm{qvB} \sin \theta

$$

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=q v B \sin 90

$$

$$

F=qvB

$$

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.

$$

d B=\frac{\mu_0 I d l \sin \theta}{4 \pi r^2}

$$

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

$$

E=F / q

$$

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

$$

\tau=m \times B

$$

In magnitude

$$\tau=m B \sin \theta$$

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