Question

Two coils, held in fixed positions, have a mutual inductance of M = 0.0034 H. The current in the first coil is I(t) = I0sin(ωt), where I0 = 5.4 A, ω = 143 rad/s.
M = 0.0034 H I0 = 5.4 A ω = 143 rad/s


(a) Express the magnitude of the induced emf in the second coil, ε2, in terms of M and I.

(b) Express the magnitude of ε2 in terms of M, Io, and ω.

(c) Express the maximum value of |ε2|, εmax, in terms of M, I0, and ω.

(d) Calculate the numerical value of εmax in V.

Answer 1

Answer

given,

I(t) = I₀ sin(ωt),  

M = 0.0034 H, I₀ = 5.4 A,  ω = 143 rad/s.

a) magnitude of induced emf in terms of M and I

    ε₂ = $-M\dfrac{dI}{dt}$

b) magnitude of induced emf in terms of M, Io, and ω

      $\dfrac{dI}{dt}=\dfrac{d}{dt}(I_0sin(\omega t))$

      $\dfrac{dI}{dt}=I_0 \omega cos (\omega t)$

now,

      ε₂ = $-MI_0 \omega cos (\omega t)$

c) maximum value of  |ε2|, εmax, in terms of M, I₀ , and ω.

       |ε₂| = $|-MI_0 \omega cos (\omega t)|$

      for ε_{max} , cos ωt = 1

       ε_{max} = $MI_0 \omega$  

d) numerical value of εmax in V.

      ε_{max} = $MI_0 \omega$  

      ε_{max} = $0.0034\times 5.4\times 143$  

      ε_{max}  = 2.63 V