A long wire carries a current of 18 ~A kept along the axis of a long solenoid of radius 1 ~cm . The field due to the solenoid is 8.0 10⁻³ ~T . The magnitude of the resultant field at a point 0.6 ~mm from the solenoid axis is (Assume, ₀=4 10⁻⁷ Tm / A )

Step-by-step solution

Given, current in a long wire, I=18 ~A magnetic field due to a solenoid, aligned & B₁=8 10⁻³ ~T & and r=0.6 ~mm =0.6 10⁻³ ~m & Radius of solenoid, R=1 ~cm =1 10⁻² ~m & Magnetic field due to current carrying wire at a & point, P & aligned B₂ & = ₀ 2 I r =2 10⁻⁷ 18 0.6 10⁻³ & =6 10⁻³ ~T (in upward direction) aligned aligned Since, current carrying wire is placed along the axis of solenoid, hence magnetic field produced by wire and magnetic field due to solenoid at point P , both are perpendicular to each other, Hence