A long straight wire carries a current of 7.0 A. What is the magnetic field strength 0.05 m away from the wire?

Question

BlackTom AI · Accepted Answer

We start by identifying the formula for the magnetic field due to a long straight current-carrying wire: B = μ0 I / (2π r), where μ0 = 4π × 10^-7 T·m/A, I is the current, and r is the distance from the wire.

Option a: 3.5 × 10^-6 T. If we plug in numbers, B = (4π×10^-7 × 7) / (2π × 0.05) = (28×10^-7) / (0.1) ≈ 2.8 × 10^-5 T. This option is off by roughly a factor of 8 compared to the correct magnitude, so it underestimates the field.

Option b: 2.8 × 10^-5 T. This matches the calculation exactly: B = (4π×10^-7 × 7) / (2π × 0.05) simplifies to (28×10^-7) / 0.1 = 2.8 × 10^-5 T. The dependence on I and 1/r is consistent with the Biot–Savart law for a long straight wire.

Option c: 7.0 × 10^-6 T. This value is smaller than the derived result by a factor of 4. It could arise if one mistakenly used a different distance or misapplied the proportionality to I, but with the given I and r, the calculation above shows this is not correct.

Option d: 1.4 × 10^-5 T. This is exactly half of 2.8 × 10^-5 T. A common error is to misplace factors of 2π or to mis-handle the denominator, but the correct algebra yields 2.8 × 10^-5 T, not half of it.

In summary, the correct expression scales linearly with current and inversely with radius, and the numerical substitution with I = 7 A and r = 0.05 m leads to 2.8 × 10^-5 T. The other options reflect plausible arithmetic slip-ups or misinterpretations of the 2π factors in the denominator.

A long straight wire carries a current of 7.0 A. What is the magnetic field strength 0.05 m away from the wire?单项选择题

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