A charged particle is projected into a region containing a uniform magnetic field B = ( j + 2 k ) T with a velocity v = (2 i + j ) m/s. The resulting acceleration of the particle is given by a = (x i - 10 j + z k ) m/s ^2 . The value of (x + z) is __________.

Step-by-step solution

The magnetic force on a moving charged particle is given by F = q( v B ) . Since the acceleration a is in the direction of the magnetic force, it must be perpendicular to both the velocity vector v and the magnetic field vector B . Therefore, the dot products of the acceleration with both velocity and magnetic field must be zero. First, applying a v = 0 : (x i - 10 j + z k ) (2 i + j ) = 0 (x)(2) + (-10)(1) + (z)(0) = 0 2x - 10 = 0 x = 5 Second, applying a B = 0 : (x i - 10 j + z k ) ( j + 2 k ) = 0 (x)(0) + (-10)(