A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at a2 and 2a from axis of the wire is :
- 4 : 1
- 3 : 4
- 1 : 1
- 1 : 4
Answer
(3) 1 : 1
Solution
Ampere's law B d l = 0 Ienc:
inside, only Ienc = I r2a2 is enclosed ⇒ B = 0 I r2 a2 (r < a); outside B = 0 I2 r (r > a)
[figure]
Ba/2 = 0 I (a/2)2 a2 = 0 I4 a
B2a = 0 I2 (2a) = 0 I4 a
Ba/2 : B2a = 1 : 1
Answer: (3)