Applications of EM Induction (AQA A Level Physics): Revision Note

Moving conductors in a magnetic field

• Similar to a coil or a solenoid, a straight conducting rod moving through a magnetic field will also have an e.m.f. induced in it

• The maximum e.m.f. is induced when the conductor moves perpendicular to the magnetic field lines, where it cuts through the greatest amount of magnetic flux

• The conducting rod has a length $L$ and moves through a uniform magnetic field with flux density $B$ at a constant velocity $v$

• The distance travelled by the conductor is:

$s=v∆t$

• Where:

  • $s$ = distance travelled (m)

  • $v$ = velocity (m s^-1)

  • $∆t$ = time interval (s)

• Therefore, the area $A$ of the magnetic flux that it cuts through is:

$A=Lv∆t$

• The total flux the conductor cuts through is:

$∆\Phi =BA=BLv∆t$

• Faraday's law gives the e.m.f. induced:

$\epsilon =N\frac{∆\Phi }{∆t}$

• Where for the conductor, $N=1$

• Substituting the change in magnetic flux $∆\Phi$ into the e.m.f. equation:

$\epsilon =\frac{BLv∆t}{∆t}$

• Therefore, the induced e.m.f. in the conductor as it moves through the magnetic field is:

$\epsilon =BLv$

• This equation shows that the e.m.f induced increases if:

  • a longer conductor is in the field

  • the magnetic field strength is larger

  • the conductor cuts through the field lines faster

EMF induced in a rotating coil

• When a coil rotates in a uniform magnetic field, the flux through the coil will vary as it rotates

• Since e.m.f is the rate of change of flux linkage, this means the e.m.f will also change as it rotates 

  • The maximum e.m.f. is when the coil cuts through the most field lines

  • The e.m.f induced is an alternating voltage

• This means that the e.m.f. is:

  • maximum when $\theta =90°$

    • The magnetic field lines are parallel to the plane of the area (or the normal to the area is perpendicular to the field lines)

  • zero when $\theta =0°$

    • The magnetic field lines are perpendicular to the plane of the area (or the normal to the area is parallel to the field lines)

• Note that this is the opposite of the maximum and minimum flux through the coil

• The flux linkage can also be written as:

$N\Phi =BAN\cos \left(\omega t\right)$

• Where the angle $\theta$ depends on the angular speed of the coil, $\omega$:

$\theta =\omega t$

• The induced e.m.f, $\epsilon$ from Faraday's Law depends on the rate of change of flux linkage, which means it can also be written as:

$\epsilon =BAN\omega \sin \left(\omega t\right)$

• Where:

  • $\epsilon$ = e.m.f induced in the coil (V)

  • $B$ = magnetic flux density (T)

  • $A$ = cross-sectional area of the coil (m²)

  • $\omega$ = angular speed of the coil (rad s^-1)

  • $t$ = time (s)

• The equation shows that the e.m.f varies sinusoidally and it is 90° out of phase with the flux linkage