Two long parallel wires are placed at x = -5 cm and x = +5 cm , parallel to the y -axis. Both wires carry currents in the +y direction of 10 A and 30 A respectively. An electron passes through the origin with a velocity v = 5 10^5 i m/s . To make the electron pass undeflected, a uniform electric field E = E₀ j is applied. The value of E₀ in V/m is

Step-by-step solution

The magnetic field at the origin due to the first wire (at x = -5 cm , current 10 A in +y direction) is into the plane ( - k ). B ₁ = ₀ I₁ 2 d (- k ) = 4 10⁻⁷ 10 2 0.05 (- k ) = -4 10⁻⁵ k T The magnetic field at the origin due to the second wire (at x = +5 cm , current 30 A in +y direction) is out of the plane ( + k ). B ₂ = ₀ I₂ 2 d (+ k ) = 4 10⁻⁷ 30 2 0.05 (+ k ) = +12 10⁻⁵ k T Net magnetic field at the origin is B = B ₁ + B ₂ = 8 10⁻⁵ k T . For the electron to pass undeflected, the net Lorentz force must be zer