A charged particle moves in a magnetic field with a velocity v = (3 i - 4 j + 2 k ) m/s. The magnetic force acting on the particle is measured to be F = (2 i + x j + 5 k ) N. The value of x is __________.

Step-by-step solution

The magnetic force acting on a moving charged particle is given by F = q( v B ) . From the properties of the cross product, the magnetic force F is always perpendicular to the velocity vector v . Therefore, the dot product of the force and velocity vectors must be zero: F v = 0 Substituting the given vectors: (2 i + x j + 5 k ) (3 i - 4 j + 2 k ) = 0 (2)(3) + (x)(-4) + (5)(2) = 0 6 - 4x + 10 = 0 16 - 4x = 0 4x = 16 x = 4 Answer: 4