A wire of radius 0.6 cm carries a current of 10 A that is uniformly distributed over its cross section.Calculate the magnetic field strength at r = 0.3 cm divided by that at r = 0.9 cm.
A)1.0
B)0.75
C)0.50
D)2.0
E)3.0

Question

Quizplus · Accepted Answer

The magnetic field strength at a distance r from a long, straight wire carrying a current I is given by:$$B = \frac{\mu_0 I}{2\pi r}$$where \mu_0 is the permeability of free space.At r = 0.3 cm, the magnetic field strength is:$$B_1 = \frac{\mu_0 I}{2\pi (0.3 	ext{ cm})}$$At r = 0.9 cm, the magnetic field strength is:$$B_2 = \frac{\mu_0 I}{2\pi (0.9 	ext{ cm})}$$The ratio of the magnetic field strength at r = 0.3 cm to that at r = 0.9 cm is:$$\frac{B_1}{B_2} = \frac{0.9 	ext{ cm}}{0.3 	ext{ cm}} = 3$$Therefore, the correct answer is B) 0.75.

A Wire of Radius 0