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Faraday’s Law of Induction (DP IB Physics)

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Katie M

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Katie M

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Faraday’s Law of Induction

  • Faraday's Law connects the rate of change of magnetic flux linkage with induced e.m.f

  • It is defined in words as:

    The magnitude of an induced e.m.f is directly proportional to the rate of change of magnetic flux linkage

  • Faraday's Law of induction is defined by the equation:

epsilon space equals space fraction numerator N open parentheses increment capital phi close parentheses over denominator increment t end fraction

  • Where:

    • epsilon = induced e.m.f (V)

    • N increment open parentheses capital phi close parentheses = change in magnetic flux linkage (Wb turns)

    • increment t = time interval (s)

  • When a coil is completely vertical relative to the magnetic field lines:

    • The change in magnetic flux linkage is at a maximum - the field lines are travelling through the area of the coil

    • There is no e.m.f induced - there is no cutting of field lines i.e. there is no change in magnetic flux linkage

  • When a coil is completely horizontal relative to the magnetic field lines:

    • The change in magnetic flux linkage is zero - there are no field lines travelling through the area of the coil

    • Maximum e.m.f is induced - there is the maximum cutting of field lines

Coil Turning E.m.f

Emf induced and the rotation of a coil

Worked Example

A small rectangular coil contains 350 turns of wire. The longer sides are 3.5 cm and the shorter sides are 1.4 cm.

4-4-2-faradays-law-worked-example

The coil is held between the poles of a large magnet so that the coil can rotate about an axis through its centre. The magnet produces a uniform magnetic field of flux density 80 mT between its poles.

The coil is positioned horizontally and then turned through an angle of 40° over a time interval of 0.18 s.

Calculate the magnitude of the average e.m.f induced in the coil.

Answer:

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

  • Angle of rotation, θ = 40°

  • Time interval, Δt = 0.18 s

 Step 2: Write down the equation for Faraday’s law:

epsilon space equals space fraction numerator N left parenthesis increment capital phi right parenthesis over denominator increment t end fraction

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 B cos θ as it rotates 

  • Therefore, the equation to use is:

N open parentheses increment capital phi close parentheses space equals space N B A cos space theta

Step 4: Determine the change in magnetic flux linkage

  • The coil is initially horizontal (θ = 0°) in the field and is rotated by 40°

  • The initial flux linkage through the coil is:

N capital phi subscript i n i t i a l end subscript space equals space N B A space cos space 0 degree space equals space 350 space cross times space left parenthesis 80 cross times 10 to the power of negative 3 end exponent right parenthesis space cross times space left parenthesis 4.9 cross times 10 to the power of negative 4 end exponent right parenthesis space cross times space 1

N capital phi subscript i n i t i a l end subscript space equals space 0.01372 space Wb

  • The final flux linkage through the coil is:

N capital phi subscript f i n a l end subscript space equals space N B A space cos space 40 degree space equals space 350 space cross times space open parentheses 80 cross times 10 to the power of negative 3 end exponent close parentheses space cross times space open parentheses 4.9 cross times 10 to the power of negative 4 end exponent close parentheses space cross times space cos space 40

N capital phi subscript f i n a l end subscript space equals space 0.01051 space Wb

  • Therefore, the change in flux linkage is:

N increment capital phi space equals space N capital phi subscript i n i t i a l end subscript space minus space N capital phi subscript f i n a l end subscript

N increment capital phi space equals space 0.01372 space minus space 0.01051 space equals space 3.21 cross times 10 to the power of negative 3 end exponent space Wb

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

epsilon space equals space fraction numerator 3.21 cross times 10 to the power of negative 3 end exponent over denominator 0.18 end fraction space equals space 0.0178 space straight V space equals space 17.8 space mV

Examiner Tips and Tricks

The important point to notice is that an emf is induced in a conductor in a magnetic field if there is change in flux linkage. This means, the conductor (e.g. a coil) must cut through the field lines to have an emf (and hence a current) induced.

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.