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The maximum working flux density of a lifting electromagnet is 1.9 T and the effective
area of a pole face is circular in cross-section. If the total magnetic flux produced is 611
mWb determine the radius of the pole face.?
area of a pole face is circular in cross-section. If the total magnetic flux produced is 611
mWb determine the radius of the pole face.?
Most Upvoted Answer
The maximum working flux density of a lifting electromagnet is 1.9 T a...
To determine the radius of the pole face of the lifting electromagnet, we can use the relationship between magnetic flux (Φ), magnetic flux density (B), and the area (A) of the pole face.
Formula for Magnetic Flux
The magnetic flux is given by the equation:
\[
Φ = B \times A
\]
Where:
- \( Φ \) = Magnetic Flux (in Weber, Wb)
- \( B \) = Magnetic Flux Density (in Tesla, T)
- \( A \) = Area of the pole face (in square meters, m²)
Given Values
- Maximum working flux density, \( B = 1.9 \, T \)
- Total magnetic flux, \( Φ = 611 \, mWb = 611 \times 10^{-3} \, Wb = 0.611 \, Wb \)
Calculate Area
Rearranging the formula to find the area:
\[
A = \frac{Φ}{B}
\]
Substituting in the values:
\[
A = \frac{0.611 \, Wb}{1.9 \, T} = 0.321 \, m²
\]
Area of Circular Cross-section
The area \( A \) of a circular cross-section is given by:
\[
A = πr^2
\]
Where \( r \) is the radius. Setting the two area equations equal:
\[
πr^2 = 0.321
\]
Solving for Radius
Rearranging for \( r \):
\[
r^2 = \frac{0.321}{π}
\]
Calculating \( r^2 \):
\[
r^2 ≈ \frac{0.321}{3.14159} ≈ 0.102 \, m²
\]
Now take the square root to find \( r \):
\[
r ≈ \sqrt{0.102} ≈ 0.319 \, m
\]
Conclusion
Thus, the radius of the pole face is approximately **0.319 meters** (or **31.9 cm**).
Formula for Magnetic Flux
The magnetic flux is given by the equation:
\[
Φ = B \times A
\]
Where:
- \( Φ \) = Magnetic Flux (in Weber, Wb)
- \( B \) = Magnetic Flux Density (in Tesla, T)
- \( A \) = Area of the pole face (in square meters, m²)
Given Values
- Maximum working flux density, \( B = 1.9 \, T \)
- Total magnetic flux, \( Φ = 611 \, mWb = 611 \times 10^{-3} \, Wb = 0.611 \, Wb \)
Calculate Area
Rearranging the formula to find the area:
\[
A = \frac{Φ}{B}
\]
Substituting in the values:
\[
A = \frac{0.611 \, Wb}{1.9 \, T} = 0.321 \, m²
\]
Area of Circular Cross-section
The area \( A \) of a circular cross-section is given by:
\[
A = πr^2
\]
Where \( r \) is the radius. Setting the two area equations equal:
\[
πr^2 = 0.321
\]
Solving for Radius
Rearranging for \( r \):
\[
r^2 = \frac{0.321}{π}
\]
Calculating \( r^2 \):
\[
r^2 ≈ \frac{0.321}{3.14159} ≈ 0.102 \, m²
\]
Now take the square root to find \( r \):
\[
r ≈ \sqrt{0.102} ≈ 0.319 \, m
\]
Conclusion
Thus, the radius of the pole face is approximately **0.319 meters** (or **31.9 cm**).
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The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.?
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The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.?.
The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The maximum working flux density of a lifting electromagnet is 1.9 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 611 mWb determine the radius of the pole face.?.
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