Two long parallel conductors S 1 and S 2 are separated by a distance 10 cm and carrying currents of 4 A and 2 A respectively. The conductors are placed along x -axis in X - Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of 3 π coulomb is passing through the point P with velocity v → = 2 i ^ + 3 j ^ m s - 1 ; where i ^ & j ^ represents unit vector along x

Step-by-step solution

Net magnetic field at P is B Net = μ 0 × i 1 2 π r 1 − μ 0 i 2 2 π r 2 - k ^ B Net   = μ 0 4 2 π × 4 100 - μ 0 2 2 π × 6 100 = μ 0 π × 100 1 2 - 1 6 = μ 0 π × 100 4 2 × 6 = μ 0 × 100 3 π - k ^ So, force acting on charge particle is F → = q v → × B → = 3 π 2 i ^ + 3 j ^ μ 0 × 100 3 π - k ^ = 4 π × 10 - 7 2 i ^ + 3 j ^ × 100 - k ^ = 4 π &#21