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

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.

1. 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} )

2. 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°).

3. 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} )

4. 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.