The direction of conventional electric current is the direction of flow of positive charge. When the electrons are moving, the conventional current is regarded as flowing in the opposite direction.

**Magnetic force on moving charge**

The size of force on the moving charge in a uniform magnetic field depends on:

- The magnetic flux density B
- The charge Q on the particle
- The speed v of particle

If the motion is at right angles to the magnetic field:

F = BQv

If the motion is at an angle θ to magnetic field;

F = BQv sinθ

If the equations F = BIL and F = BQv are consistent with one another;

Since current I is rate of flow of charge;

I = Q/t

Substituting,

F = BQL/t

Now L/t is the speed so,

F = BQv

For an electron, with a charge –e the magnitude of force is;

F = Bev

The force on moving charge is sometimes called Bev force.

**Orbiting Charge**

When a charged particle moves at right angles to a uniform magnetic field, magnetic force F is always perpendicular to its velocity, hence F acts as a centripetal force (force directed towards the center of the circle);

Centripetal force = mv^{2}/r

The centripetal force is provided by the magnetic force Bev. Therefore

Bev = mv^{2}/r

Cancelling;

R = mv/Be

The equation when rewritten in terms of momentum p of the particle is;

P = Ber

** The charge to mass ratio of an electron**

It involves finding the charge to mass ratio e/m known as specific charge on the electron.

e/m_{e} = v/Br

B and r are measurable but v is not;

eV_{ca }= ½ m_{e}v^{2}

Where m_{e} is the electron mass and v is speed

e/m_{e} = 2V_{ca}/r^{2}B^{2}

**Hall Effect**

The hall-effect is another mechanism in which the mechanism in which the electric and magnetic forces in the moving charged particle is balanced.

The production of voltage across a conductor when a current flows through the conductor at right angle to magnetic field. The charge detected by a small voltage across the probe is hall voltage. The greater the magnetic flus density, the greater the hall voltage.

The electric field strength E is related to the Hall voltage V_{H}:

E = V_{H}/d

Equating electric and magnetic forces

eE = Bev

Substituting,

eV_{H}/d = Bev

By substituting v from I = nAve where A is cross sectional area of conductor and n is number density of conducting particles;

eV_{H}/d = BeI/nAe

V_{H} = Bid/nAe

V_{H = }BI/nte

V_{H} = BI/ntq

Positive charged particles will be deflected in the opposite direction to negative charge and so we determine whether the charge particle are negative or positive by using hall voltage.