Question 6.6: A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s −1 in a uniform horizontal magnetic field of magnitude 3.0×10 −2 T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10Ω, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?Class 12 - Physics - Electromagnetic Induction Electromagnetic Induction Page-230

Question 6.6: A circular coil of radius 8.0 cm and 20 turns is rotated

1.	Question 6.6: A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s −1 in a uniform horizontal magnetic field of magnitude 3.0×10 −2 T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10Ω, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?Class 12 - Physics - Electromagnetic Induction Electromagnetic Induction Page-230
Answer» Given, Radius of the circular COIL,r = 8.0 cm = 0.08 m No. of turns in the coil, N =20 Angular frequency ω = 50 rad/s Magnitude of magnetic field B =3.0 × 10^-2 T Resistance of the closed loop = 10 Ω The area of the coil can be calculated using the formula A =πr² = 3.14 × (0.08 m)² The maximum induced e.m.f is calculated as follows:e = NωAB e = 20 × 50 rad/s × 3.14 × (0.08 m)² × 3.0 × 10^–2 T e = 0.603 V For a complete cycle, the average induced EMF will be zero. The maximum current for the circular coil can be calculated as follows: I = e/R Substituting the values I = 0.603 V/10 Ω I = 0.0603A The average power loss due to Joule’s HEATING effect in the circular coil will be given by: P = (ei)/2 P = (0.603 V × 0.0603 A)/2 P = 0.018 W.

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