The magnetic field in a region varies as shown in the figure. Determine the average induced emf in a conducting loop of area 2.0 10⁻³ m ^2 oriented perpendicular to the field, for each of the four 10 ms intervals depicted.

Step-by-step solution

The average induced emf in a loop is given by Faraday's law of induction: _ avg = - t = -A B t where A = 2.0 10⁻³ m ^2 is the area of the loop and t = 10 ms = 10⁻² s is the time interval. For the first interval ( 0 to 10 ms ): B₁ = 0.01 - 0 = 0.01 T ₁ = -(2.0 10⁻³) 0.01 10⁻² = -0.002 V = -2.0 mV For the second interval ( 10 to 20 ms ): B₂ = 0.03 - 0.01 = 0.02 T ₂ = -(2.0 10⁻³) 0.02 10⁻² = -0.004 V = -4.0 mV For the third interval ( 20 to 30 ms ): B₃ = 0.01 - 0.03 = -0.02 T ₃ = -(2.0 10⁻³) -0.02 10⁻² = 0.004 V = 4.0