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Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is?
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Long straight wire carrying a current produces magnetic induction of 4...
Understanding the Magnetic Field Around a Long Straight Wire
A long straight wire carrying an electric current generates a magnetic field around it, which can be calculated using the formula:
B = (μ₀ * I) / (2 * π * r)
Where:
- B is the magnetic induction (in Tesla),
- μ₀ is the permeability of free space (approximately 4π x 10^-7 Tm/A),
- I is the current (in Amperes),
- r is the distance from the wire (in meters).
Given Values
- Magnetic induction (B) = 4 x 10^-6 T
- Distance (r) = 15 cm = 0.15 m
Rearranging the Formula
To find the current (I), we can rearrange the formula:
I = (B * 2 * π * r) / μ₀
Substituting the Values
- μ₀ = 4π x 10^-7 Tm/A
- r = 0.15 m
Now, substituting these values into the rearranged formula:
- I = (4 x 10^-6 T * 2 * π * 0.15 m) / (4π x 10^-7 Tm/A)
The π cancels out, simplifying the equation:
- I = (4 x 10^-6 T * 0.3 m) / (4 x 10^-7 Tm/A)
Calculating the Current
This reduces to:
- I = (1.2 x 10^-6 Tm) / (4 x 10^-7 Tm/A)
- I = 3 A
Conclusion
The current flowing through the wire is 3 Amperes. This demonstrates the relationship between the current, the magnetic field it generates, and the distance from the wire. Understanding this principle is essential for applications in electromagnetism and electrical engineering.
A long straight wire carrying an electric current generates a magnetic field around it, which can be calculated using the formula:
B = (μ₀ * I) / (2 * π * r)
Where:
- B is the magnetic induction (in Tesla),
- μ₀ is the permeability of free space (approximately 4π x 10^-7 Tm/A),
- I is the current (in Amperes),
- r is the distance from the wire (in meters).
Given Values
- Magnetic induction (B) = 4 x 10^-6 T
- Distance (r) = 15 cm = 0.15 m
Rearranging the Formula
To find the current (I), we can rearrange the formula:
I = (B * 2 * π * r) / μ₀
Substituting the Values
- μ₀ = 4π x 10^-7 Tm/A
- r = 0.15 m
Now, substituting these values into the rearranged formula:
- I = (4 x 10^-6 T * 2 * π * 0.15 m) / (4π x 10^-7 Tm/A)
The π cancels out, simplifying the equation:
- I = (4 x 10^-6 T * 0.3 m) / (4 x 10^-7 Tm/A)
Calculating the Current
This reduces to:
- I = (1.2 x 10^-6 Tm) / (4 x 10^-7 Tm/A)
- I = 3 A
Conclusion
The current flowing through the wire is 3 Amperes. This demonstrates the relationship between the current, the magnetic field it generates, and the distance from the wire. Understanding this principle is essential for applications in electromagnetism and electrical engineering.
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Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is?
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Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is?.
Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Long straight wire carrying a current produces magnetic induction of 4 x 10-6 T at a point 15 cm from the wire. The current through the wire is?.
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