V = kq/r

Definition

The equation V = kq/r represents the electric potential at a point in space due to a point charge. It describes the relationship between the electric potential (V), the charge (q), the distance from the charge (r), and the Coulomb constant (k).

5 Must Know Facts For Your Next Test

1. The electric potential at a point due to a point charge is inversely proportional to the distance from the charge, as indicated by the 1/r term in the equation.
2. The electric potential is directly proportional to the magnitude of the charge, as indicated by the q term in the equation.
3. The Coulomb constant, k, is a physical constant that has a value of approximately 8.99 × 10^9 N⋅m^2/C^2.
4. The electric potential at a point is a scalar quantity, meaning it has a magnitude but no direction.
5. The electric potential is measured in units of volts (V), which is the same unit as the potential energy per unit charge.

Review Questions

• Explain how the electric potential at a point is related to the charge and distance from the charge according to the equation V = kq/r.
  • The electric potential at a point is directly proportional to the magnitude of the charge and inversely proportional to the distance from the charge. As the charge increases, the electric potential increases linearly. As the distance from the charge increases, the electric potential decreases inversely, following the 1/r relationship. The Coulomb constant, k, is a scaling factor that relates the electric potential to the charge and distance.
• Describe the physical significance of the Coulomb constant, k, in the equation V = kq/r.
  • The Coulomb constant, k, is a fundamental physical constant that relates the magnitude of the electrostatic force between two point charges to their charges and the distance between them. In the equation V = kq/r, the Coulomb constant serves as a scaling factor that converts the charge and distance information into the appropriate units for electric potential, which is measured in volts. The value of the Coulomb constant is approximately 8.99 × 10^9 N⋅m^2/C^2, indicating the strength of the electrostatic interaction between charges.
• Analyze how the electric potential, V, would change if the distance, r, between the point charge and the observation point were doubled, while the charge, q, remained constant.
  • If the distance, r, between the point charge and the observation point were doubled, while the charge, q, remained constant, the electric potential, V, would decrease by a factor of 4. This is because the equation V = kq/r shows that the electric potential is inversely proportional to the distance, r. Doubling the distance would result in the 1/r term becoming 1/(2r), which is 1/4 of the original value. Therefore, the electric potential would decrease by a factor of 4 when the distance is doubled, while the charge remains constant.

Related terms

Electric Potential:

The electric potential at a point in space is the work per unit charge required to move a test charge from infinity to that point.

Coulomb Constant: The Coulomb constant, represented by the symbol k, is a physical constant that relates the magnitude of the electrostatic force between two point charges to their charges and the distance between them.

Point Charge:

A point charge is an idealized model of a charge that is concentrated at a single point in space, with no spatial extent.