A long straight wire carrying a current of 30 ~A is placed in an external uniform magnetic field of induction 4 10⁻⁴ ~T . The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point 2.0 ~cm away from the wire is ( ₀=4 10⁻⁷ H / m )

Step-by-step solution

i=30 ~A , B=4 10⁻⁴ ~T r=2 ~cm =2 10⁻² ~m Initial magnetic field (parallel to the wire), B₁=4 10⁻⁴ ~T Magnetic field produced by the straight wire, B₂= ₀ i 2 r = 2 10⁻⁷ 30 2 10⁻² =3 10⁻⁴ ~T B₂ will be in the plane perpendicular to the plane of wire, so B₁ and B₂ are perpendicular to each other. Resultant magnetic field, B= B₁^2+B₂^2 = (4 10⁻⁴ )^2+ (3 10⁻⁴ )^2 =5 10⁻⁴