What is the magnetic field due to a straight wire at a distance of 0.5 m carryin

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Question: What is the magnetic field due to a straight wire at a distance of 0.5 m carrying a current of 10 A?

Options:

Correct Answer: 0.4 μT

Solution:

Using B = μ₀I/(2πr), substituting μ₀ = 4π × 10⁻⁷ Tm/A, I = 10 A, and r = 0.5 m gives B = 0.4 μT.

What is the magnetic field due to a straight wire at a distance of 0.5 m carrying a current of 10 A?

What is the magnetic field due to a straight wire at a distance of 0.5 m carrying a current of 10 A?

Step 1: Identify the formula for the magnetic field (B) around a straight wire: B = μ₀I/(2πr).
Step 2: Note the values you need to substitute into the formula: μ₀ = 4π × 10⁻⁷ Tm/A, I = 10 A, and r = 0.5 m.
Step 3: Substitute the values into the formula: B = (4π × 10⁻⁷ Tm/A * 10 A) / (2π * 0.5 m).
Step 4: Simplify the equation: B = (4 × 10⁻⁷ * 10) / (2 * 0.5).
Step 5: Calculate the numerator: 4 × 10⁻⁷ * 10 = 4 × 10⁻⁶.
Step 6: Calculate the denominator: 2 * 0.5 = 1.
Step 7: Divide the numerator by the denominator: B = 4 × 10⁻⁶ / 1 = 4 × 10⁻⁶ T.
Step 8: Convert the result to microteslas (μT): 4 × 10⁻⁶ T = 0.4 μT.

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