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A magnetic field is passing through a loop of wire whose area is 0.025 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 0.22 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 (a), at what rate (in m^2/s) should the area be changed at the instant when B

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Answer:

a) The magnitude of the emf induced is 0.0055 V

b) The rate should the are be changed is 0.0037 m²/s

Explanation:

a) The magnitude of the emf induced in the loop is equal to:

[tex]E=A\frac{dB}{dt} =0.025*0.22=0.0055V[/tex]

b) The induced emf is equal to:

[tex]V=B\frac{dA}{dt} +A\frac{dB}{dt} \\0=1.5\frac{dA}{dt} +0.0055\\\frac{dA}{dt} =-0.0037m^{2} /s[/tex]

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