The magnetic field of a wire and of a loop
Answers are for parents and teachers.
1
A long straight wire carries 35 A in air. Find B at 14 cm from it.
d = 0.14 m. B = 2 × 10⁻⁷ × 35 ÷ 0.14 = 5 × 10⁻⁵ T.
2
At what distance from a wire carrying 10 A in air is B = 2.5 × 10⁻⁵ T?
d = 2 × 10⁻⁷ × I ÷ B = (2 × 10⁻⁷ × 10) ÷ (2.5 × 10⁻⁵) = 0.08 m = 8 cm.
3
One point is 4 cm from a long straight wire and another is 12 cm from it. Compare the flux densities there.
B follows 1 ÷ d. The point at 4 cm is three times nearer than the one at 12 cm (12 ÷ 4 = 3), so B at 4 cm is three times B at 12 cm.
4
A coil has 200 turns, a radius of 8 cm and carries 0.6 A. Find B at its centre (π = 3.14).
r = 0.08 m. B = 6.28 × 10⁻⁷ × 200 × 0.6 ÷ 0.08 = 6.28 × 10⁻⁷ × 1500 = 9.42 × 10⁻⁴ T.
5
One point is 3 cm from a long straight wire carrying 4 A, and another point is 9 cm from a long straight wire carrying 15 A, both in air. At which point is the flux density larger, and by what ratio?
B is proportional to I ÷ d. First point: 4 ÷ 3 = 1.33. Second point: 15 ÷ 9 = 1.67 (same units). So B is larger at the second point, by the ratio 1.67 ÷ 1.33 = 1.25.