Question

A generator contains a 100-turn coil that rotates 10.0 times per second. If each turn has an area of 0.100 m2 and the magnetic field through the coils is 0.050 T, what is the maximum emf induced in the coil? 62.8 V 6.28 V 31.4 V 3.14 V 0.314 V

Answer 1

To solve this problem we will apply the concepts related to the electric potential induced by a magnetic field. Mathematically it can be defined as the product between the number of loops, the magnetic field, the cross-sectional area and the angular velocity. Thus

$\epsilon_{max} = NBA\omega$

Here,

N = Number of Loops

B = Magnetic Field

A = Cross-Sectional Area

$\epsilon_{max} = (100)(0.05T)(0.1m^2)(10\frac{rev}{s} \frac{2\pi rad}{1rev})$

$\epsilon_{max}=31.4 Volts$

Therefore the induced voltage is 31.4V

Answer 2

Answer:

emf=-10V

Explanation:

the emf can be calculated by using the expression

$\epsilon=-N\frac{\Delta \Phi_B}{\Delta t}\\\Phi_B=BS$

where Ф is the magnetic flux and S is the area of the turns.

we can take that in one half of the period, we have the maximum and minimum of the flux. Hence

$T=\frac{1}{f}=\frac{1}{10}=0.1s$

Thus, we have

$\epsilon=-(100)\frac{(0.05T)(0.100m^2)}{\frac{0.1s}{2}}=10V$

hope this helps!!