# Flash Cards

Magnetism

## The direction of the magnetic force on a positive charge

Version 1 (right hand rule): point fingers of your right hand in the direction of $\vec v$ and curl them (through the smaller angle) toward $\vec B$. Your upright thumb shows the cross product $\vec v \times \vec B$ or the magnetic force $\vec F_B$. This force is perpendicular to the plane of $\vec v-\vec B$

Version 2 (right hand rule): point your fingers in the direction of $\vec B$ so the thumb points toward the velocity $\vec v$, the magnetic force on a positive charge is in the outward direction of your palm.

Note: the magnetic force on a negative charge is in opposite direction to that given right hand rule.

Magnetism

## Drawing the field lines

To draw the magnetic field lines around a magnet or other magnetic objects, one can use the alignment of compass needle near those.

The direction of these lines, in a magnet outside it, is away from N pole toward the S pole.

Using small iron filing one can display magnetic field patterns around magnetic objects.

The compass needles using its alignment with the magnetic field find shows the direction of the magnetic fields.

Magnetism

## Motion of a charged particle in a uniform magnetic field

When the velocity of a charged particle $\vec v$ is perpendicular to a uniform $\vec B$, the particle moves around a circle in a plane perpendicular to $\vec B$.

There is always a centripetal force in a circular path, which in this case provided by magnetic force, therefore the radius of the circular path is
$\underbrace{qvB}_{F_B}=\frac{mv^{2}}{r} \quad \Rightarrow \quad r=\frac{mv}{qB}$

The time required to particle travel one circle or the peri

Magnetism

## Charged particle in magnetic field

If a particle of charge q and velocity $\vec v$ enters a region of space occupied by magnetic field $\vec B$, which is establishes by some source, it experiences a magnetic force $\vec F_B$ given by
$\vec F_B=q\vec v \times \vec B$
Using definition of the cross product, we obtain its magnitude as
$|\vec F_B|=|q|vB\, \sin \theta$
Where $\theta$ is the smaller angle between $\vec v$ and $\vec B$.

Magnetism

## Magnetic field

1. The space around a magnet where the forces of attraction or repulsion on a magnetic object can be detected is called magnetic field.
2. Magnetic field around a magnet or other magnetic object is visualized by magnetic field lines.
3. Magnetic field around a magnet or other magnetic object can be displayed by iron filling patterns.
4. Magnetic field around a magnet or other magnetic object can be detected by a little compass needle at that point.
5. Small compass needle is aligned parallel to the magnetic field, with the north pole of the compass shows the direction of the magnetic field at that point.
6. The direction

Magnetism

## Properties of magnetic force

(1) The magnitude of a magnetic force depends only on the magnitude of the charge i.e. $F\propto |q|$

(2)  Magnetic force is always perpendicular to the plane containing $\vec v$ and $\vec B$.

(3)  A charge moving parallel $\theta=0$ to a magnetic field experiences zero magnetic force.

(4)  A charge moving perpendicular $\theta =90{}^\circ$ to a magnetic field experiences a maximum magnetic force $F_B=qvB$.

(5)  The magnetic force on a positively charge particle is in opposite direction to that of a negatively charge particle i.e. $\vec F_{B(q)}=\vec F_{B(-q)}$

Magnetism

## Difference between electric and magnetic forces

(1) Electric force does work on a rest or moving charge but magnetic force does only work on moving charge.

(2) The electric force vector is along the direction of electric field $\vec E$, whereas the magnetic force is perpendicular to the plane of $\vec v-\vec B$.

(3) The electric force can change the speed or kinetic energy of a particle but magnetic force can alter only the direction of the velocity of particle.