Two long parallel wires W₁ and W₂ are placed in the x-y plane at y = 5 cm and y = -5 cm respectively, parallel to the x -axis. Wire W₁ carries a current of 2 A in the +x direction, and W₂ carries an unknown current I in the -x direction. A particle with charge q = 2 mC passes through the origin with velocity v = 5 10^4 ( i + j ) m/s . If the magnetic force acting on the particle is F = -2.4 10⁻³ ( i - j ) N , the val

Step-by-step solution

The magnetic field at the origin due to wire W₁ (at y = 5 cm , current in +x direction) is into the plane ( - k ). B ₁ = ₀ I₁ 2 d (- k ) = 4 10⁻⁷ 2 2 0.05 (- k ) = -8 10⁻⁶ k T The magnetic field at the origin due to wire W₂ (at y = -5 cm , current in -x direction) is also into the plane ( - k ). B ₂ = ₀ I 2 d (- k ) = 4 10⁻⁷ I 2 0.05 (- k ) = -4I 10⁻⁶ k T Net magnetic field at the origin is B = -(8 + 4I) 10⁻⁶ k T . The magnetic force is F = q( v B ) . v B = 5 10^4 ( i + j ) [-(8 + 4I) 10⁻⁶ k ] v B = -0.05 (8 + 4I)