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When a charged particle, like a bullet with a net electric charge, moves through a magnetic field, it experiences a force known as the Lorentz force. This force is given by the formula:

• \( F = qvB \sin(\theta) \)

where:

• \( F \) is the magnetic force.
• \( q \) is the charge of the particle.
• \( v \) is the velocity of the particle.
• \( B \) is the magnetic field strength.
• \( \theta \) is the angle between the velocity and the direction of the magnetic field.

Since the bullet moves perpendicular to the Earth's magnetic field, the angle \( \theta \) is \( 90^\circ \), simplifying the equation to:

• \( F = qvB \)

This makes the computation straightforward, assuming the charge, velocity, and magnetic field are known. The Lorentz force causes the charged particle to follow a curved path. The extent of this curvature depends on factors like the field strength and the particle's velocity.

The kinematic equations are used to predict the motion of objects when they are subjected to forces. In this case, once the Lorentz force is calculated, the next step is to find the resulting acceleration. Using Newton's second law:

• \( F = ma \)

The acceleration \( a \) is:

• \( a = \frac{F}{m} \)

where \( m \) is the mass of the bullet. With the acceleration known, kinematic equations help in finding the deflection. The kinematic equation for distance traveled under constant acceleration is:

• \( d = \frac{1}{2}at^2 \)

Here, \( d \) is the deflection distance, \( a \) is the acceleration due to the magnetic force, and \( t \) is the time taken to travel a particular distance, like 1 km in this scenario. By understanding how acceleration due to an external force changes an object's path, these equations allow us to solve for the resulting movement.

When a charged particle such as a bullet travels through the Earth's magnetic field, it does not follow a straight-line path but instead gets slightly deflected. This deflection occurs because of the Lorentz force acting perpendicular to its motion. The path becomes slightly curved due to this sideway force. To determine how much the bullet deflects, it's important to recognize that the deflection distance depends largely on:

• The magnetic force acting on the bullet.
• The time the bullet spends in the magnetic field.
• The bullet's initial velocity which dictates how quickly it covers ground.

All of these aspects can be calculated using the given physics equations. By combining the Lorentz force understanding with kinematic principles, the deflection over a given distance can be effectively predicted. Practically, this helps us anticipate how charged particles deviate from their path in magnetic fields, a principle applied in various fields like physics experiments and electronic devices.