Question

Scientific work is currently underway to determine whether weak oscillating magnetic fields can affect human health. For example, one study found that drivers of trains had a higher incidence of blood cancer than other railway workers, possibly due to long exposure to mechanical devices in the train engine cab. Consider a magnetic field of magnitude 1.00 times 10^-3 T oscillating sinusoidal at 50.5 Hz. If the diameter of a red blood cell is 7.00 mu m, determine the maximum emf that can be generated around the perimeter of a cell in this field. _____________ V

Answer 1

Answer:

$E_{max}$= 6.11 10⁻¹² V

Explanation:

For this exercise we must use the Faraday equation

    E = - d Φ / dt

    Φ = B . A = B A cos θ

The area of ​​a red blood cell that we can consider circular is

    A = π R²

The magnetic field has the form

    B = B₀ sin (w t)

Suppose the red blood cell is parallel to the field, the angle is zero and the cos 0º = 1. In blood cell size it is constant, so we can take out the area of ​​the integral.

    E = -A dB / dt

    E = -A B₀ w cos wt

For maximum electromotive force cos θ = ± 1

    $E_{max}$ = A Bo w

    w = 2π f

    R = d / 2

    $E_{max}$ = pi (d /2)² B₀ 2π f

    $E_{max}$ = ¼ π² d² B₀ f

Let's calculate

    $E_{max}$ = ¼ π² (7.00 10⁻⁶)² 1.00 10⁻³ 50.5

   $E_{max}$= 6.11 10⁻¹² V