Exam Notes 4.4 & 4.5

The Motor Effect

A current-carrying wire in a magnetic field experiences a force. The force F is given by F = BIL, where B is the magnetic flux density (in Tesla), I is the current (in Amperes), and L is the length of the wire (in meters). Fleming's Left Hand Rule determines the direction of the force.

Practical: Finding Magnetic Flux Density

To find magnetic flux density: Place a magnet on a balance, tare the balance, measure the 'mass' when a known current is flowing, convert to Newtons, measure the length of the wire in the field, and rearrange F = BIL to solve for B.

Free Charged Particle

A charge moving in a magnetic field experiences a force perpendicular to its velocity, resulting in circular motion. The force is given by F = BQv, where Q is the charge and v is the velocity. For electrons or +1 ions, F = Bev. The radius of the circular path is r = \frac{mv}{BQ}, where m is the mass. The frequency is independent of the radius.

Cyclotron

Cyclotrons use F = BQv to produce beams of charged particles. Particles undergo circular motion inside 'dees,' and the polarity of the dees reverses to accelerate particles across the gap, increasing their speed and radius. The frequency is f = \frac{BQ}{2\pi m}, and all protons have the same frequency regardless of radius.

Mass Spectrometer

Mass spectrometers separate ions based on their mass. A velocity selector ensures all ions have the same speed. The radius of the ion path is r = \frac{mv}{BQ}. A sensor array detects ions of specific masses to obtain relative abundance. In the velocity selector, only ions for which the forces due to the magnetic field and electric field are balanced pass through, i.e., BQv = EQ, so v = \frac{E}{B}.

Induction

Flux (\phi) is a measure of 'how much magnetism' passes through an area and is given by \phi = BA. Flux linkage is \,N\phi = NBA. An EMF is induced in a wire experiencing a changing magnetic field. Faraday's Law states that induced emf is proportional to the rate of change of flux linkage: \,\varepsilon = -N \frac{\Delta \phi}{\Delta t}. Lenz's Law states that the direction of induced emf/current opposes the change causing it. For a moving wire, \varepsilon = BLv. For static coils, if AC is used E = - \frac{\Delta (BA)}{\Delta t} A