A 10 g bullet having a charge of 4.00 μC is fired at a speed of 270 ms–1 in a horizontal direction. A vertical magnetic field of 500 μT exists in the space. Find the deflection of the bullet due to the magnetic field as it travels through 100 m. Make appropriate approximations.


Given-



Mass of the bullet, m = 10g = 10-3 Kg



Charge of the bullet, q = 4.00 μC =10-6 C



Speed of the bullet in horizontal direction, v = 270 m/s



Vertical magnetic field, B = 500 μT = 500× 10-6 T



Distance travelled by the bullet, d = 100 m



Magnetic force,


We know, Lorentz force F is given by -



where,


q = charge


v = velocity of the charge


B=magnetic field


and


θ= angle between V and B


Also,



And Newton's second law of motion



where m = mass


a= acceleration


Using equation (1) –





we know



⇒



Substituting the values, time taken by the bullet to travel 100 m horizontally,



Applying 2nd equation of motion


where,


a= acceleration


u = initial velocity


t= Time taken to cross the magnetic field


Since, the initial velocity is zero,


from (1),(2) and (3)



Now, the deflection caused by the magnetic field in this time


interval,





1