alleryStart learning →How much current must a long straight wire carry to create a field of 1.0 x 10^-4 T at a distance of 5.0 cm from it?
A50 A
B2.5 A
C250 A
D25 A
Answer & Solution
Correct answer: D. 25 A
1. Start from B = mu0 I / (2 pi r) and solve for the current: I = 2 pi r B / mu0.
2. Convert the distance: 5.0 cm = 5.0 x 10^-2 m.
3. Substitute: I = 2 pi (5.0 x 10^-2 m)(1.0 x 10^-4 T) / (4 pi x 10^-7 T m/A).
4. The factor pi cancels between the top and the bottom.
5. The numerator becomes 2 x 5.0 x 10^-6 = 1.0 x 10^-5, and the denominator becomes 4 x 10^-7.
6. Dividing gives I = 25 A.
7. So a moderately large current is enough to produce twice the field of the Earth at 5.0 cm.
8. An answer of 50 A comes from dropping the factor 2 pi on one side only.
_Source: OpenStax College Physics (CC BY 4.0), Ch 22 "Magnetism", section 22.9 Magnetic Fields Produced by Currents: Ampere's Law_
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