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A magnetic field is passing through a loop of wire whose area is 0.026 m2. The direction of the magnetic field is parallel to the normal to the loop, and the magnitude of the field is increasing at the rate of 0.24 T/s. (a) Determine the magnitude of the emf induced in the loop. (b) Suppose the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part

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Answer:

a) 6.24 × 10⁻³ V

b) 4.16 × 10⁻³ m²/s

Explanation:

Given that:

(a)

Area A = 0.026 m²

[tex]\dfrac{dB}{dt}=0.24 \ T/s[/tex]

[tex]e=\dfrac{d\phi}{dt} \\ \\ = \dfrac{d}{dt}(BA) \\ \\ =A\dfrac{dB}{dt} \\\\= 0.026 \times 0.24 \\ \\ = 0.00624\ V \\ \\ \mathbf{= 6.24 \times 10^{-3} \ V}[/tex]

(b)

[tex]Here; \\ \\ e =0\\\\ \dfrac{d}{dt}(BA) =0 \\ \\ \implies B\dfrac{dA}{dt}+ A\dfrac{dB}{dt} = 0 \\ \\ B\dfrac{dA}{dt}= -A\dfrac{dB}{dt} \\ \\ \dfrac{dA}{dt}= -\dfrac{A}{B} \dfrac{dB}{dt} \\ \\ = -\dfrac{0.026}{1.5}\times 0.24 \\ \\ \dfrac{dA}{dt}= 4.16 \times 10^{-3}\ m^2/s[/tex]