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.]

Step-by-step solution

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