A charge particle is moving in a uniform magnetic field 2 i ^ + 3 j ^ T . If it has an acceleration of α i ^ - 4 j ^ m s - 2 , then the value of α will be

Step-by-step solution

The magnetic force on a moving charged particle is given by F → = q v → × B → . Therefore, we know that the magnetic force is perpendicular to the magnetic field. Therefore, the resulting acceleration will also be perpendicular to the magnetic field. As the scalar product of two mutually perpendicular vectors is zero, ⇒ a → · B → = 0   ⇒ α i ^ - 4 j ^ · 2 i ^ + 3 j ^ = 0 ⇒ 2 α - 12 = 0 ⇒ α = 6