Intensity and charge

Question

A square coil of side L = 0.1 m and resistance R = 100Ω lying in the horizontal plane is subject to a magnetic field B(t) = Bo sinωt directed vertically (Bo = 0.3 T, ω = 50π Hz). Question.

Determine:

1) the intensity of the induced current flowing in the coil at the time 2π/3ω;

2) the charge Q flowing through the coil from t = 0 up to t=2π/3ω.

Answer 1

We are using Faraday's Law: φ=BA = B₀L² sin(ωt), ΙεΙ = B₀L²ω cos(ωt), I = ΙεΙ/R = B₀L²ω/R cos(ωt)

At, t = 2π/3ω, I = B₀L²ω/R cos(2π/3) = 0.002356 A

I = dQ/dt, dQ = I dt, Q = integral (B₀L²ω/R cos(ωt) dt) from 0 to 2π/3ω = (B₀L²ω/R)(1/ω)sin(ω2π/3ω) -(B₀L²ω/R)(1/ω)sin(ω·0)=B₀L²/R·sin(2π/3) = 2.6 ·10^-5 C