A charge particle is moving in a uniform magnetic field (2iˆ+3jˆ)T. If it has an acceleration of (αiˆ−4jˆ)m/s2, then the value of α will be :

The force on a charged particle moving in a magnetic field is given by the Lorentz force law, which states that F = q(v x B), where F is the force, q is the charge, v is the velocity, and B is the magnetic field.

However, the force is also equal to the mass times acceleration (F = ma), where m is the mass and a is the acceleration.

Setting these two equal to each other gives q(v x B) = ma.

The acceleration is given as (αiˆ−4jˆ)m/s2, and the magnetic field is given as (2iˆ+3jˆ)T.

The cross product of the velocity and the magnetic field (v x B) will be perpendicular to both the velocity and the magnetic field. Since the acceleration is not in the same direction as the magnetic field, this implies that the velocity must be in a direction that is not parallel to the magnetic field.

Without knowing the direction of the velocity, we cannot solve for α. We would need additional information about the direction and magnitude of the velocity to solve for α.