An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field B . The magnitude of the line integral B d l along a straight line from the point (- 3 a, a, 0) to (a, a, 0) is given by [ _0 is the magnetic permeability of free space.]
A. 7 _0 I / 24
aligned & | d |= rd \\ & | B |= _0 I 2 r \\ & B d = | B || d | 0^ \\ & = ( _0 I 2 r ) ( rd ) \\ & = _ _1 ^ _2 _0 I 2 d = _0 I 2 [ _2- (- _1 ) ] aligned [ _1 is anticlockwise hence taken negative] aligned & _1= a 3 a = 3 \\ & _1= 3 \\ & _2= a a =1 \\ & _2= 4 \\ & B d = _0 I 2 [ 3 + 4 ] \\ & = 7 _0 I 24 \\ & Ans. Option (1) aligned
Related: Physics — Magnetic Effects of Current · All PYQ Banks