If a wire carries a current of 5 A, what is the magnetic field at a distance of 0.1 m from the wire?

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Q: If a wire carries a current of 5 A, what is the magnetic field at a distance of 0.1 m from the wire?

Solution: Using Ampere's Law, B = μ₀I/2πr, where μ₀ = 4π × 10^-7 Tm/A, we find B = (4π × 10^-7)(5)/(2π(0.1)) = 0.1 T.

Steps: 10

Step 1: Identify the current (I) flowing through the wire, which is given as 5 A.
Step 2: Identify the distance (r) from the wire where we want to find the magnetic field, which is given as 0.1 m.
Step 3: Use the formula for the magnetic field (B) around a long straight wire: B = μ₀I / (2πr).
Step 4: Identify the value of μ₀ (the permeability of free space), which is 4π × 10^-7 Tm/A.
Step 5: Substitute the values into the formula: B = (4π × 10^-7 Tm/A)(5 A) / (2π(0.1 m)).
Step 6: Simplify the equation: B = (4 × 10^-7 × 5) / (2 × 0.1).
Step 7: Calculate the numerator: 4 × 5 = 20, so we have B = (20 × 10^-7) / (0.2).
Step 8: Calculate the denominator: 0.2 = 2 × 10^-1.
Step 9: Divide: B = (20 × 10^-7) / (2 × 10^-1) = 10 × 10^-6 = 0.1 T.
Step 10: Conclude that the magnetic field at a distance of 0.1 m from the wire is 0.1 T.