Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
A circular coil of one turn with a radius of 5.0 cm is rotated about a diameter at a constant angular speed of 80 revolutions per minute. A uniform magnetic field B = 0.010 T exists in a direction perpendicular to the axis of rotation. Determine the maximum emf induced.
Options
- A6.6 10⁻⁴ V
- B3.3 10⁻⁴ V
- C1.3 10⁻³ V
- D4.2 10⁻⁴ V
Correct answer
A. 6.6 10⁻⁴ V
Step-by-step solution
The maximum induced emf in a rotating coil is given by the formula: _ max = NAB Given parameters are: Number of turns, N = 1 Radius, r = 5.0 cm = 0.05 m Area, A = r^2 = (0.05)^2 = 0.0025 m ^2 Magnetic field, B = 0.010 T Angular speed, = 80 rev/min = 80 2 60 rad/s = 8 3 rad/s Substituting these values into the formula: _ max = 1 (0.0025 ) 0.010 ( 8 3 ) _ max = 25 10⁻⁶ 8 3 _ max = 200 ^2 3 10⁻⁶ Using ^2 9.87 : _ max 200 9.87 3 10⁻⁶ 6.58 10⁻⁴ V Rounding off, we get 6.6 10⁻⁴ V .