Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centres P and Q of a semicircular arc are B1 and B2 respectively, then the ratio B1B2 is . [figure]
- 2+ 1+
- 1+ 1-
- 2+ 1-
- 1+ 2-
Answer
(1) 2+ 1+
Solution
Field at the centre of a semicircular arc: 0I4r
Field of a semi-infinite wire at a point at distance r from its end, on the perpendicular through the end: 0I4 r
Fig. (I): two semi-infinite wires (each at distance r from P) + semicircle; by the right-hand rule all three fields at P point the same way (out of the page).
B1= 0I4 r+ 0I4 r+ 0I4r= 0I4 r(2+ )
Fig. (II): the vertical wire starts at the lowest point of the arc, directly below Q, so Q lies on its line ⇒ its field at Q is zero.
B2= 0I4 r+ 0I4r= 0I4 r(1+ )
B1B2= 2+ 1+
Answer: (1)