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A coil with 20 circular turns each of diameter 60 mm is placed in a uniform magnetic field of flux density 90 mT - AQA - A-Level Physics - Question 22 - 2017 - Paper 2
Question 22
A coil with 20 circular turns each of diameter 60 mm is placed in a uniform magnetic field of flux density 90 mT. Initially the plane of the coil is perpendicular t... show full transcript
Worked Solution & Example Answer:A coil with 20 circular turns each of diameter 60 mm is placed in a uniform magnetic field of flux density 90 mT - AQA - A-Level Physics - Question 22 - 2017 - Paper 2
Step 1
What is the emf induced in the coil?
Answer
To calculate the emf induced in the coil, we can use Faraday's law of electromagnetic induction, which states that the induced emf ( ext{emf} = -N \frac{d\Phi}{dt} ) where:
- ( N ) is the number of turns in the coil (20 turns),
- ( \Phi ) is the magnetic flux, and
- ( dt ) is the time interval for the change in flux.
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Calculate the initial magnetic flux (( \Phi_i )): The magnetic flux is given by: ( \Phi = B \cdot A ) where:
- ( B ) is the magnetic flux density (90 mT = 0.09 T), and
- ( A ) is the area of the coil given by ( A = \pi r^2 ), with ( r = 30 , \text{mm} = 0.03 , ext{m} ). Thus: ( A = \pi (0.03)^2 = 0.002827 , \text{m}^2 ) Therefore: ( \Phi_i = 0.09 , \text{T} \cdot 0.002827 , \text{m}^2 \approx 0.00025443 , \text{Wb} )
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Calculate the final magnetic flux (( \Phi_f )): When the coil is parallel to the field lines, the magnetic flux is: ( \Phi_f = 0 , \text{Wb} ) (since the angle between the magnetic field and the area vector is 90°).
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Calculate the rate of change of flux (( \frac{d\Phi}{dt} )): ( \frac{d\Phi}{dt} = \frac{\Phi_f - \Phi_i}{dt} = \frac{0 - 0.00025443}{0.20} \approx -0.00127215 , \text{Wb/s} )
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Calculate the induced emf: Using Faraday's law: ( \text{emf} = -N \frac{d\Phi}{dt} = -20 \times (-0.00127215) \approx 0.0254 , \text{V} = 25.4 , \text{mV} ) Thus, rounding the answer to the nearest significant figure gives: Answer: 25 mV, which corresponds to option C.