IDNLearn.com is your go-to platform for finding reliable answers quickly. Join our interactive Q&A community and access a wealth of reliable answers to your most pressing questions.
Sagot :
We are being given that:
- The length of a metal blade = 300 cm
- The angular velocity at which the metal blade is rotating about its axis is ω = 17 rad/s
- The magnetic field (B) = 4.0 mT
A pictorial view showing the diagrammatic representation of the information given in the question is being attached in the image below.
From the attached image below, the potential difference across the conducting element of the length (dx) moving with the velocity (v) appears to be perpendicular to the magnetic field (B).
The magnitude of the potential difference induced between the center of the blade in relation to either of its ends can be determined by using the derived formula from Faraday's law of induction which can be expressed as:
[tex]\mathsf{E = B\times l\times v}[/tex]
where;
- B = magnetic field
- l = length
- v = relative speed
From the diagram, Let consider the length of the conducting element (dx) at a distance of length (x) from the center O.
Then, the velocity (v) = ωx
The potential difference across it can now be expressed as:
[tex]\mathsf{dE = B*(dx)*(\omega x)}[/tex]
For us to determine the potential difference, we need to carry out the integral form from center point O to L/2.
∴
[tex]\mathsf{E = \int ^{L/2}_{0}* B (\omega x ) *(dx)}[/tex]
[tex]\mathsf{E = B (\omega ) \times \Big[ \dfrac{x^2}{2}\Big]^{L/2}_{0}}[/tex]
[tex]\mathsf{E = B (\omega ) * \Big[ \dfrac{L^2}{8}\Big]}[/tex]
Recall that,
- magnetic field (B) = 4 mT = 4 × 10⁻³ T
- Length L = 300 cm = 3m
- angular velocity (ω) = 17 rad/s
[tex]\mathsf{E = (4\times 10^{-3}) * (17) \Big[ \dfrac{(1.5)^2}{8}\Big]}[/tex]
[tex]\mathsf{E = 19.13 mV}[/tex]
Thus, we can now conclude that the magnitude of the potential difference as a result of the rotation caused by the metal blade from the center to either of its ends is 19.13 mV.
Learn more about Faraday's law of induction here:
https://brainly.com/question/13369951?referrer=searchResults

Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.