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A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T?
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A long straight wire(radius=3mm) carries a constant current distribute...
Calculation of Magnetic Field on the Axis of the Wire
The magnetic field on the axis of the wire can be calculated using the Biot-Savart Law, which states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current, length of the wire, and inversely proportional to the distance from the wire.
- Formula: B = μ₀I/2πr
- Here, B - magnetic field, μ₀ - magnetic constant (4π×10^-7 Tm/A), I - current, and r - distance from the wire.
Substituting the given values, we get:
- For r = 0 (on the axis): B = μ₀I/2πr = ∞ (as r → 0)
- For r = 2mm: B = μ₀I/2πr = (4π×10^-7 Tm/A) × (100 A/m^2) / (2π × 0.002 m) = 10^-4 T
- For r = 4mm: B = μ₀I/2πr = (4π×10^-7 Tm/A) × (100 A/m^2) / (2π × 0.004 m) = 9π/2 × 10^-8 T
Answer: Option (1) 2π×10^-8 T, 9π/2 ×10^-8 T
Explanation:
- The magnetic field on the axis of the wire is infinite as the distance from the wire approaches zero.
- As the distance from the wire increases, the magnetic field decreases and follows an inverse square law.
- At a distance of 2mm from the wire, the magnetic field is 10^-4 T, which is the highest value in the given options.
- At a distance of 4mm from the wire, the magnetic field is 9π/2 × 10^-8 T, which matches with option (1).
The magnetic field on the axis of the wire can be calculated using the Biot-Savart Law, which states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current, length of the wire, and inversely proportional to the distance from the wire.
- Formula: B = μ₀I/2πr
- Here, B - magnetic field, μ₀ - magnetic constant (4π×10^-7 Tm/A), I - current, and r - distance from the wire.
Substituting the given values, we get:
- For r = 0 (on the axis): B = μ₀I/2πr = ∞ (as r → 0)
- For r = 2mm: B = μ₀I/2πr = (4π×10^-7 Tm/A) × (100 A/m^2) / (2π × 0.002 m) = 10^-4 T
- For r = 4mm: B = μ₀I/2πr = (4π×10^-7 Tm/A) × (100 A/m^2) / (2π × 0.004 m) = 9π/2 × 10^-8 T
Answer: Option (1) 2π×10^-8 T, 9π/2 ×10^-8 T
Explanation:
- The magnetic field on the axis of the wire is infinite as the distance from the wire approaches zero.
- As the distance from the wire increases, the magnetic field decreases and follows an inverse square law.
- At a distance of 2mm from the wire, the magnetic field is 10^-4 T, which is the highest value in the given options.
- At a distance of 4mm from the wire, the magnetic field is 9π/2 × 10^-8 T, which matches with option (1).
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A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T?
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A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T?.
A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long straight wire(radius=3mm) carries a constant current distributed uniformly over a cross section perpendicular axis of the wire. If the current density is 100 A/m^2. The magnitude of the magnetic field at (a) 2mm from the axis of the wire and (b) 4mm from the axis of the wire is (1) 2π×10^-8 T, 9π/2 ×10^-8 T (2) 4π ×10^-8 T, π/2×10^-8 T (3) 4π×10^-8 T, 9π/2×10^-8 T (4) π×10^-4 T, 9π/2×10^-8 T?.
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