Q. 465.0( 1 Vote )

A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and having a charge 1.0 × 10–5 C projected from south to north so that it moves with a uniform velocity?

Answer :

Given-


Magnetic field, B = 0.20 T


Mass of the particle, m = 0.010 g = 1 × 10−5 kg


Charge of the particle, q = 1.0 × 10−5 C


Given in the question that, if the particle has to move with


uniform velocity in the region of the applied field,


the gravitational force experienced by the particle must be


equal to the magnetic force experienced by the particle.


Gravitational force,



where


m is the massof theobject


g=acceleration due to gravity


And


Magnetic force, we know, Lorentz force F is given by -



where,


q = charge on an electron


v = velocity of the electron


B=magnetic field


θ= angle between B and v


So,






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