Compute the magnitude of the electric field and the absolute...

Compute the magnitude of the electric field and the absolute potential at a distance of $1.0 \mathrm{~nm}$ from a helium nucleus of charge $+2 e$. What is the potential energy (relative to infinity) of a proton at this position?

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Key Concepts

Electric Potential Energy in an Electric Field

Electric potential energy is defined as the energy a charge possesses due to its position within an electric potential field. It is calculated by multiplying the charge by the electric potential (U = qV). This concept is essential for determining the energy interactions between charges, such as the energy required to bring a positive test charge, like a proton, into the vicinity of another charge.

Electric Field due to a Point Charge

This concept involves using Coulomb’s law to determine the strength and direction of an electric field produced by a point charge. The electric field at a distance r from a charge q is given by E = k|q|/r², where k is Coulomb’s constant. It quantifies how a charge influences the space around it, and how a test charge placed in that field would experience a force.

Electric Potential due to a Point Charge

The electric potential at a distance r from a point charge is a scalar quantity calculated using V = kq/r. It represents the work done per unit charge in bringing a charge from infinity to that point in the electric field created by the source charge. The concept is critical for understanding energy considerations in electrostatics.

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