• If the interval of time becomes very small (i.e., in the limit of Δt?→ 0) the equation for Faraday's Law can be written as:

Combining Lenz's Law and Faraday's Law

• Combining Lenz's Law into the equation for Faraday's Law is written as:

• The?negative?sign?represents Lenz's Law
  • This is because it shows the induced e.m.f?ε?is set up in an 'opposite?direction' to oppose the changing flux linkage

• This equation also shows that the?gradient of the graph of magnetic flux (linkage) against time, ?represents the?magnitude?of the induced e.m.f
  • Note: the negative sign means if the gradient is?positive, the induced e.m.f is?negative
  • This is again due to Lenz's Law, which says the e.m.f is set up to?oppose?the effects of the changing flux linkage

Step 1: Write down the known quantities

• • Magnetic flux density,?B?= 80 mT = 80 × 10-3?T
  • Area,?A?= 3.5 × 1.4 = (3.5 × 10-2) × (1.4 × 10-2) = 4.9 × 10-4?m2
  • Number of turns,?N?= 350
  • Time interval, Δt?= 0.18 s

?Step 2:?Write out the equation for Faraday’s law:

Step 3: Write out the equation for the change in flux linkage:

• • The number of turns?N?and the coil area?A?stay constant
  • The flux through the coil changes as it rotates
  • Therefore, the change in flux linkage can be written as:

Δ(NΦ) =?NA(ΔB)

Step 4: Determine the change in magnetic flux linkage

• • The initial flux through the coil is zero (flux lines are parallel to the coil face)
  • The final flux through the coil is 80 mT (flux lines are perpendicular to the coil face)
  • This is because the coil begins horizontally in the field and is rotated 90°
  • Therefore, the change in flux linkage is:

Δ(NΦ) =?NA(ΔB) = 350 × (4.9 × 10-4) × (80 × 10-3) = 0.014 Wb turns

Step 5: Substitute change in flux linkage and time into Faraday’s law equation:

= 0.076 V