91Ó°ÊÓ

Kinetic energy is the energy associated with the motion of an object. In the world of physics, it's a crucial concept because it allows us to understand how energy transforms from one form to another. For an object moving at a certain velocity, the kinetic energy is calculated using the formula: \[ KE = \frac{1}{2}mv^2 \]In this exercise, the particle starts from rest, meaning its initial kinetic energy is zero. As it moves 6.00 cm in the electric field, it gains kinetic energy amounting to \(1.50 \times 10^{-6} \text{ J}\). This increase is a direct result of the work done by the electric force on the particle, demonstrating the profound relationship between work and kinetic energy.

• Increases when an object speeds up
• Directly affected by changes in velocity

Electric potential reflects the potential energy per unit charge at a particular location in an electric field. Think of it as the electric version of gravitational potential energy. When a charge moves in an electric field, especially over a certain distance, it undergoes a change in electric potential. In this scenario, the work done on the charge translates into a potential difference or voltage \( \Delta V\). The electric potential helps us quantify how much energy a charge can gain or lose when moving between two points. The relationship between the work done \( W \) and change in electric potential is given by:\[ W = q \Delta V \] Rearranging the formula allows us to solve for the change in electric potential:\[ \Delta V = \frac{W}{q} \]Upon plugging in the given values, we find that \( \Delta V \approx 357.14 \text{ V} \).

• Provides insight into energy changes in a field
• Measured in volts, representing energy per charge unit

Work done in the context of physics is the energy transferred to or from an object via a force acting over a displacement. For electric fields, the work done by the field on a charge results in a change in the charge's kinetic energy. Here, since the particle started from rest, the entire kinetic energy of \(1.50 \times 10^{-6} \text{ J}\) is due to the work done by the electric force. This demonstrates the principle:\[ W = \Delta KE \] which tells us that work done equals the change in kinetic energy. This relationship emphasizes the interchangeable nature of work and energy within physics. In an electric field setting, if we know the work done, we immediately can deduce changes in kinetic energy and vice versa.

• Energy transfer via force
• Indicator of energy transformation across systems

Electric potential energy is the energy stored in a system of charges due to their positions within an electric field. This energy is particularly important when charges are displaced, as in our exercise. Here, a charged particle shifts within the field, leading to changes in its potential energy.The formula for potential energy change in an electric field is similar to that for electric work and is given by:\[ \Delta U = q \Delta V \] For the particle in question, \[ \Delta U = 4.20 \times 10^{-9} \text{ C} \times 357.14 \text{ V} = 1.50 \times 10^{-6} \text{ J} \] This calculation mirrors the outcome of the work done because potential and kinetic energies are interlinked through conservation of energy.

• Energy based on charge configuration
• Subject to changes as charges relocate