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11 Electromagnetic Induction (Magnetic Flux \(\phi\) (Single Coil (When…
11 Electromagnetic Induction
Questions
Nov 15 Q8 P2
Nov 16 Q10
Nov 18
Magnetic Flux \(\phi\)
Single Coil
When cross-sectional area \(\perp\) magnetic field
\(\phi=BA\)
When area not \(\perp\)
\(\phi=BA\cos\theta\)
Unit:
Webers
(Wb)
Solenoid
\(\phi=NBA\cos\theta\)
Moving
Straight Wire
\(\phi=Blx=Blv\Delta t\)
Magnetic Field strength
its like magnetic flux per area
Unit:
Tesla
(T)
Induced EMF \(\epsilon\)
Faraday's Law
Induced emf is directly proportional to change of magnetic flux linkage \(\phi\) with time
\(\epsilon =-N\frac{\Delta\phi}{\Delta t}\)
'-' sign is from Lenz Law
Moving
Straight Wire
Since \(\phi=Blx\)
\(\epsilon=\frac{Bl\Delta x}{\Delta t}\)
\(\epsilon=Blv\)
Rectangular or
Circular Coil
No induced current
when coil is moving inside
Induced current when one coil is outside the field
Use RH rule for
determining
current (UP)
Treat each side
as a wire
Right hand Rule
Used for finding
induced current
AC Generator
Increase in speed
of rotation :runner:
Increase frequency
Increase amplitude :zap:
of induced e.m.f
\(\epsilon=-\frac{d}{dt}\phi\)
If coil is vertical at
\(t=0\)
\(\epsilon=-\frac{d}{dt}NBA\cos(\omega t)\)
\(\epsilon =\omega NBA\sin(\omega t)\)
AC
RMS
value of the direct current that dissipates power in a resistor at the same rate.
Power
Average Power
\(P_{avg}=\frac{P_{max}}{2}\)
\(\frac{V_0I_0}{2}=\frac{V_0}{\sqrt{2}}\cdot\frac{I_0}{\sqrt{2}}=V_{rms}\cdot I_{rms}\)
Maximum Power
\(P_{max}=V_0I_0\)
\(V_0\): peak voltage
\(I_0\): peak current
Rectification
Transformers
Lenz Law
:one:
:arrow_right: force causes induced current to flow :arrow_double_up: through wire (RH rule)
:two:
Induced current :arrow_double_up: leads to induced :arrow_left: magnetic force (LH rule)
\(l\): Length of wire
\(x\): Distance travelled by wire
