91Ó°ÊÓ

Electric force, a fundamental concept in electromagnetism, acts on a charged particle when it is placed in an electric field. Imagine a field similar to gravity, but instead of pulling everything down, this electric field applies a force depending on whether the charge is positive or negative.

For a positive charge, the electric force direction aligns with the electric field's direction, like in this exercise where both the field and the force are in the same line. Conversely, a negative charge would move in the opposite direction. The strength or magnitude of this force depends on both the charge amount and the field strength itself.

• The formula used to determine electric force is:
  \( F_e = qE \)
• Where \( q \) represents the charge and \( E \) the magnitude of the electric field.
• In the exercise, the electric force is calculated to be \( 8.28 \text{~N} \), using the charge \( 1.8 \times 10^{-6} \text{~C} \) and electric field \( 4.6 \times 10^{3} \text{~N/C} \).

Understanding these principles helps clarify why and how forces act on charges within electric fields, which is crucial for solving many physics problems.

Magnetic force plays a pivotal role when a charged particle moves through a magnetic field. In this context, the force generated is perpendicular to both the direction of the magnetic field and that of the moving charge. This perpendicular relationship stems from the nature of magnetic forces, following the right-hand rule often mentioned in physics.

In practical terms,

• The magnetic force formula is expressed as:
  \( F_m = qvB \)
• Where \( q \) is the charge, \( v \) is the velocity of the particle, and \( B \) is the strength of the magnetic field.

During the exercise, the magnetic force was computed to be \( 6.696 \text{~N} \), using the given values of \( q = 1.8 \times 10^{-6} \text{ C} \), \( v = 3.1 \times 10^{6} \text{ m/s} \), and \( B = 1.2 \times 10^{-3} \text{ T} \).

This demonstrates how magnetic fields influence moving charges, resulting in forces that are crucial for applications like electric motors and magnetic resonance imaging.

The net force experienced by a charged particle moving through electric and magnetic fields is a combination of the electric force and the magnetic force. Since both forces act perpendicular to each other in our exercise scenario, the net force is calculated using the Pythagorean theorem, which applies to right-angle vector addition.

Simply put, the net force determination requires that:

• We use the formula:
  \( F_{net} = \sqrt{F_e^2 + F_m^2} \)
• Where \( F_e \) and \( F_m \) are the magnitudes of the electric and magnetic forces, respectively.

In this case, with \( F_e = 8.28 \text{~N} \) and \( F_m = 6.696 \text{~N} \), this gives us the total force \( F_{net} \approx 10.65 \text{~N} \).
This final calculation shows how two independent forces can combine to create a resultant force that dictates the movement of the charge, an important consideration in the analysis and design of systems involving electromagnetic forces.