Question

A generator consists of a square coil with sides of 0.2 meters, wrapped 20 times being spun in a magnetic field of 0.3 Tesla. The maximum EMF generated by it is 82 volts. With what frequency, in Hz, was the coil spun?

Answer 1

Answer 2

Calculating the Rotational Frequency (f) of the Coil

Given:

• Side length of square coil (L) = 0.2 m

• Number of turns (N) = 20

• Magnetic field strength (B) = 0.3 T

• Maximum EMF (ε_max) = 82 V

• 
  

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Step 1: Determine the Area of the Coil

The coil is square, so its area ($A$) is:

$$A=L^2=(0.2\text{m}{)}^2=0.04{\text{m}}^2$$

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Step 2: Relate Maximum EMF to Frequency

The maximum EMF generated in a rotating coil is given by:

$${\epsilon }_{\text{max}}=N\cdot B\cdot A\cdot \omega$$

where:

• $\omega =2\pi f$ (angular frequency in rad/s)

• $f$ = rotational frequency in Hz

Substitute $\omega$:

$${\epsilon }_{\text{max}}=N\cdot B\cdot A\cdot (2\pi f)$$

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Step 3: Solve for Frequency (f)

Rearrange the equation to solve for $f$:

$$f=\frac{{\epsilon }_{\text{max}}}{N\cdot B\cdot A\cdot 2\pi }$$

Plug in the values:

$$f=\frac{82}{20\times 0.3\times 0.04\times 2\pi }$$$$f=\frac{82}{0.48\pi }\approx \frac{82}{1.508}\approx 54.38\text{Hz}$$

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Answer:

The coil was spun at a frequency of 54.4 Hz (rounded to 3 significant figures).