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A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T?
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A Long straight wire ( radius =3.0mm) carries a constant current distr...
Given:
- Radius of the wire (r) = 3.0 mm = 0.003 m
- Current density (J) = 100 A/m²
- Distance from the axis of the wire (d) = 4.0 mm = 0.004 m
To Find:
The magnitude of the magnetic field at a distance of 4.0 mm from the axis of the wire.
Formula:
The magnetic field (B) due to a long straight wire at a distance (d) from the wire can be calculated using Ampere's Law:
B = μ₀ * J * (2πr)
Where:
- B is the magnetic field
- μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A)
- J is the current density
- r is the radius of the wire
- d is the distance from the wire
Calculation:
Substituting the given values in the formula:
B = (4π × 10⁻⁷ T·m/A) * (100 A/m²) * (2π * 0.003 m)
Simplifying:
B = (4π × 10⁻⁷ T·m/A) * (100 A/m²) * (6π × 10⁻³ m)
B = 24π² × 10⁻⁷ × 10⁻³ T
B = 24π² × 10⁻¹⁰ T
Approximating the value of π as 3.14:
B ≈ 24 * (3.14)² × 10⁻¹⁰ T
B ≈ 24 * 9.8596 × 10⁻¹⁰ T
B ≈ 236.63 × 10⁻¹⁰ T
B ≈ 2.3663 × 10⁻⁸ T
Rounding off to the appropriate number of significant figures:
B ≈ 2.4 × 10⁻⁸ T
Therefore, the magnitude of the magnetic field at a distance of 4.0 mm from the axis of the wire is approximately 2.4 × 10⁻⁸ T, which is closest to option (4) 4π × 10⁻⁸ T.
- Radius of the wire (r) = 3.0 mm = 0.003 m
- Current density (J) = 100 A/m²
- Distance from the axis of the wire (d) = 4.0 mm = 0.004 m
To Find:
The magnitude of the magnetic field at a distance of 4.0 mm from the axis of the wire.
Formula:
The magnetic field (B) due to a long straight wire at a distance (d) from the wire can be calculated using Ampere's Law:
B = μ₀ * J * (2πr)
Where:
- B is the magnetic field
- μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A)
- J is the current density
- r is the radius of the wire
- d is the distance from the wire
Calculation:
Substituting the given values in the formula:
B = (4π × 10⁻⁷ T·m/A) * (100 A/m²) * (2π * 0.003 m)
Simplifying:
B = (4π × 10⁻⁷ T·m/A) * (100 A/m²) * (6π × 10⁻³ m)
B = 24π² × 10⁻⁷ × 10⁻³ T
B = 24π² × 10⁻¹⁰ T
Approximating the value of π as 3.14:
B ≈ 24 * (3.14)² × 10⁻¹⁰ T
B ≈ 24 * 9.8596 × 10⁻¹⁰ T
B ≈ 236.63 × 10⁻¹⁰ T
B ≈ 2.3663 × 10⁻⁸ T
Rounding off to the appropriate number of significant figures:
B ≈ 2.4 × 10⁻⁸ T
Therefore, the magnitude of the magnetic field at a distance of 4.0 mm from the axis of the wire is approximately 2.4 × 10⁻⁸ T, which is closest to option (4) 4π × 10⁻⁸ T.
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A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T?
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A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T?.
A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Long straight wire ( radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. if current density is 100A/m2. the magnitude of the magnetic field at 4.0 mm from the axis of the wire is - (1) 3π/2×10^-8 T (2) π/2 ×10^-8T (3) 9π/2 × 10^-8T (4) 4π × 10 ^ -8T?.
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