Magnetic Force on a Current

F = B I L

F is force measured in newtons (N)

B is flux density (the strength of a magnetic field I.e No. of magnetic lines of force from magnet per unit area) measured in teslas (T, named after Nikola Tesla)

I is current measured in amperes (A)

L is the length of conductor in the magnetic field measured in metres (m)

B = F/IL This defines flux density, B.

We can measure F using the current balance.

If the current cuts across the magnetic field at the angle θ then the component the current across the field is ISineθ and therefore -

F = B I L sinθ

θ is the angle the current makes with the magnetic field.

F (force) is at its maximum when θ = 90 degrees, F = 0 when the current is parallel to the field lines. i.e., θ = 0 degrees.

Use Fleming's left hand rule for the direction of motion.

Magnetic Force on a moving charge

F=BIL

= BQL/T= BQV

The SI unit for charge, Q, is coulombs - C.

If charge moving at right angles to the field

F = -Bev for an electron ( e = charge on an electron)

Remember that the direction of conventional current is opposite to that of the electron.

The magnitude of an electron charge is -1.6Ε-19

Orbiting charges

F is always perpendicular to the path of the charged particle, so the particle moves in a circular path.

Therefore, centripetal force = mv²/R = BeV

Radius of path = R = mv/Be

Parallel Current Carrying Conductors

F/l=k (I₁ I₂)/d

Where F = Force; Newtons N

l = Length of the current carrying conductors parallel to each other.

k = constant; mu0/2p = 2 x 10-7 SI Units

I₁ and I₂ are current carrying conductors respectively

d = distance between the current carrying conductors (mm)

Quick note

Radius is large for more massive, faster particles. Radius is smaller when the magnetic field strength is large