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A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis?
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A wire of a length 0.26m is bent to form a circular loop.If 2A current...
**Calculating the Magnetic Field Due to a Current-Carrying Loop**
To calculate the magnetic field due to a current-carrying loop at a point, we can use Ampere's law. Ampere's law states that the magnetic field (B) at a point due to a current-carrying wire is directly proportional to the current (I) passing through the wire and inversely proportional to the distance (r) from the wire.
**Given Data:**
- Length of the wire (l) = 0.26 m
- Current through the loop (I) = 2A
- Distance from the center of the loop to the point P (r) = 0.15 m
**Step 1: Calculating the Magnetic Field at the Center of the Loop**
At the center of the loop, the magnetic field due to the loop will be maximum. The formula for the magnetic field at the center of the loop is given as:
B_center = (μ₀ * I) / (2 * R)
Where:
- B_center is the magnetic field at the center of the loop.
- μ₀ is the permeability of free space, which is a constant with a value of 4π * 10^-7 Tm/A.
- I is the current flowing through the loop.
- R is the radius of the loop.
Since the loop is circular, the radius (R) is equal to half the length of the wire:
R = l / (2π)
Substituting the values, we can calculate the magnetic field at the center of the loop.
**Step 2: Calculating the Magnetic Field at Point P**
To calculate the magnetic field at point P, we can use the formula for the magnetic field due to a current-carrying loop at an axial point:
B = (μ₀ * I * R²) / (2 * (R² + r²)^(3/2))
Where:
- B is the magnetic field at point P.
- μ₀ is the permeability of free space.
- I is the current flowing through the loop.
- R is the radius of the loop.
- r is the distance from the center of the loop to point P.
Substituting the given values, we can calculate the magnetic field at point P.
**Step 3: Substituting the Values and Calculating the Magnetic Field at Point P**
Substituting the given values into the equation, we get:
B = (4π * 10^-7 Tm/A * 2A * (0.26m / (2π))^2) / (2 * ((0.26m / (2π))^2 + (0.15m)^2)^(3/2))
Calculating the above expression will give us the magnetic field at point P.
By following these steps and performing the necessary calculations, you can find the magnetic field due to the current-carrying loop at point P.
To calculate the magnetic field due to a current-carrying loop at a point, we can use Ampere's law. Ampere's law states that the magnetic field (B) at a point due to a current-carrying wire is directly proportional to the current (I) passing through the wire and inversely proportional to the distance (r) from the wire.
**Given Data:**
- Length of the wire (l) = 0.26 m
- Current through the loop (I) = 2A
- Distance from the center of the loop to the point P (r) = 0.15 m
**Step 1: Calculating the Magnetic Field at the Center of the Loop**
At the center of the loop, the magnetic field due to the loop will be maximum. The formula for the magnetic field at the center of the loop is given as:
B_center = (μ₀ * I) / (2 * R)
Where:
- B_center is the magnetic field at the center of the loop.
- μ₀ is the permeability of free space, which is a constant with a value of 4π * 10^-7 Tm/A.
- I is the current flowing through the loop.
- R is the radius of the loop.
Since the loop is circular, the radius (R) is equal to half the length of the wire:
R = l / (2π)
Substituting the values, we can calculate the magnetic field at the center of the loop.
**Step 2: Calculating the Magnetic Field at Point P**
To calculate the magnetic field at point P, we can use the formula for the magnetic field due to a current-carrying loop at an axial point:
B = (μ₀ * I * R²) / (2 * (R² + r²)^(3/2))
Where:
- B is the magnetic field at point P.
- μ₀ is the permeability of free space.
- I is the current flowing through the loop.
- R is the radius of the loop.
- r is the distance from the center of the loop to point P.
Substituting the given values, we can calculate the magnetic field at point P.
**Step 3: Substituting the Values and Calculating the Magnetic Field at Point P**
Substituting the given values into the equation, we get:
B = (4π * 10^-7 Tm/A * 2A * (0.26m / (2π))^2) / (2 * ((0.26m / (2π))^2 + (0.15m)^2)^(3/2))
Calculating the above expression will give us the magnetic field at point P.
By following these steps and performing the necessary calculations, you can find the magnetic field due to the current-carrying loop at point P.
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A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis?
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A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis?.
A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of a length 0.26m is bent to form a circular loop.If 2A current flowing through this loop calculate the magnetic field due to this loop at a point P which is at a distance of 0.15m from its centre on its axis?.
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