Answer:

Part a)

Average EMF for half cycle is

[tex]E_{avg} = 2.64 V[/tex]

Part b)

For one complete cycle we will have

[tex]E_{avg} = 0[/tex]

Part c)

Maximum induced EMF will be at

t = 0.025 s and 0.075 s

minimum induced EMF is at

t = 0.05s and 0.1 s

Explanation:

As we know that magnetic field is oscillating in direction as well as magnitude

so induced EMF is given as

[tex]E = NBA\omega sin(\omega t)[/tex]

Part a)

For average value of EMF from positive maximum to negative maximum which is equal to half cycle

so we have

[tex]E_{avg} = NBA\omega \frac{2}{T}\int_0^{T/2} sin(\omega t) dt[/tex]

[tex]E_{avg} = \frac{2NBA\omega}{\pi}[/tex]

[tex]E_{avg} = \frac{2(10)(0.12)(0.055)(2\pi (10))}{\pi}[/tex]

[tex]E_{avg} = 2.64 V[/tex]

Part b)

For one complete cycle we will have

[tex]E_{avg} = NBA\omega \frac{1}{T}\int_0^T sin(\omega t) dt[/tex]

[tex]E_{avg} = 0[/tex]

Part c)

Maximum induced EMF will be at

[tex]t = \frac{T}{4} and \frac{3T}{4}[/tex]

here we know

[tex]T = \frac{1}{f} = 0.1 s[/tex]

t = 0.025 s and 0.075 s

minimum induced EMF is at

[tex]t = \frac{T}{2} and T[/tex]

so it is

t = 0.05s and 0.1 s

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