The magnetic flux through each loop of 35 loop coilis given by (3.6t — 0.71t³) x10–2 Tm², where the time t is in seconds. Determine the induced emf at t equals to 5.0s
To determine the induced emf, we need to calculate the rate of change of the magnetic flux with respect to time (dφ/dt) at t = 5.0s.
Given: Magnetic flux through each loop (φ) = (3.6t – 0.71t³) x 10–2 Tm²
Taking the derivative of the magnetic flux with respect to time:
dφ/dt = (d/dt)(3.6t – 0.71t³) x 10–2 Tm²
Differentiating the terms:
dφ/dt = (3.6(1) – 0.71(3t²)) x 10–2 Tm²
dφ/dt = (3.6 – 2.13t²) x 10–2 Tm²
Now we can calculate the value of dφ/dt at t = 5.0s:
dφ/dt = (3.6 – 2.13(5)^2) x 10–2 Tm²
dφ/dt = (3.6 – 2.13(25)) x 10–2 Tm²
dφ/dt = (3.6 – 53.25) x 10–2 Tm²
dφ/dt = (-49.65) x 10–2 Tm²
dφ/dt = -0.4965 Tm²/s
The induced emf (ε) is given by Faraday's law:
ε = -N(dφ/dt)
Given that there are 35 loops (N = 35):
ε = -(35)(-0.4965 Tm²/s)
ε = 17.36 T/s
Therefore, the induced emf at t = 5.0s is 17.36 T/s.