The force acting on a charged particle moving in a magnetic field is given by the Lorentz force equation: \[ \vec{F} = q (\vec{v} \times \vec{B}) \] Where:
- \( \vec{F} \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( \vec{v} \) is the velocity vector of the particle,
- \( \vec{B} \) is the magnetic field vector.
For a negative charge, the direction of force is opposite to that predicted by the right-hand rule. Using the right-hand rule, point your fingers in the direction of the velocity vector (\(\vec{v}\), which is upward) and curl them in the direction of the magnetic field vector (\(\vec{B}\), which is towards the North).
Your thumb will point in the direction of the force on a positive charge.
Since the particle is negative, the force on the particle will be in the opposite direction to the thumb.
For this case, the force is directed towards the East.
Thus, the particle is deflected towards East.
A solid cylinder of mass 2 kg and radius 0.2 m is rotating about its own axis without friction with angular velocity 5 rad/s. A particle of mass 1 kg moving with a velocity of 5 m/s strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will be: