A 10 g bullet carrying a charge of 4.00 C is fired horizontally at a speed of 270 m s ⁻¹ . A vertical magnetic field of 500 T is present in the region. Determine the deflection of the bullet caused by the magnetic field over a travel distance of 100 m . Use appropriate approximations.

Step-by-step solution

The magnetic force acting on the bullet is perpendicular to its velocity and is given by F = qvB . The acceleration of the bullet due to this magnetic force is a = F m = qvB m . Since the deflection is very small, the horizontal velocity remains approximately constant. The time taken to travel a horizontal distance x is t = x v . The deflection y caused by the magnetic field is given by the second equation of motion: y = 1 2 at^2 = 1 2 ( qvB m ) ( x v )^2 = qBx^2 2mv Substituting the given values: q = 4.00 10⁻⁶ C B