The change in electric potential (ΔV) between two points in an electric field is proportional to the charge (q) and inversely proportional to the distances (r_1 and r_2) from the charge to those points. The constant of proportionality is the electric field constant (k).
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The change in electric potential, ΔV, is directly proportional to the charge, q, and inversely proportional to the distances, r_1 and r_2, from the charge to the two points.
The electric field constant, k, is a fundamental physical constant that appears in the expression for the change in electric potential.
The inverse square law governs the relationship between the change in electric potential and the distances from the charge, where the potential decreases as the square of the distance increases.
The change in electric potential, ΔV, represents the work done per unit charge in moving a test charge between the two points in the electric field.
The expression ΔV = kq(1/r_1 - 1/r_2) is derived from the definition of electric potential and the inverse square law governing electric forces.
Review Questions
Explain how the change in electric potential, ΔV, is related to the charge, q, and the distances, r_1 and r_2, from the charge to the two points.
The change in electric potential, ΔV, is directly proportional to the charge, q, and inversely proportional to the distances, r_1 and r_2, from the charge to the two points. This relationship is expressed by the equation ΔV = kq(1/r_1 - 1/r_2), where k is the electric field constant. As the charge increases, the change in potential increases linearly. However, as the distances from the charge increase, the change in potential decreases inversely, following the inverse square law. This means that the potential difference between two points in an electric field is highly dependent on the geometry and the charge distribution.
Describe the role of the electric field constant, k, in the expression for the change in electric potential.
The electric field constant, k, is a fundamental physical constant that appears in the expression for the change in electric potential, ΔV = kq(1/r_1 - 1/r_2). The value of k is approximately $8.99 \times 10^9 \ N\cdot m^2/C^2$, and it relates the electric force between two charges to their distance, as described by the inverse square law. The constant k serves to convert the units of the charge, q, and the distances, r_1 and r_2, into the appropriate units for the change in electric potential, which is measured in volts (V). Without the inclusion of the electric field constant, k, the expression would not correctly represent the relationship between the charge, distances, and the change in electric potential.
Analyze how the change in electric potential, ΔV, is affected by changes in the charge, q, and the distances, r_1 and r_2, from the charge to the two points.
The change in electric potential, ΔV, is directly proportional to the charge, q, and inversely proportional to the distances, r_1 and r_2, from the charge to the two points. This means that as the charge increases, the change in potential increases linearly. However, as the distances from the charge increase, the change in potential decreases inversely, following the inverse square law. For example, if the charge is doubled, the change in potential will also double. Conversely, if the distance from the charge to one of the points is increased by a factor of 2, the change in potential will decrease by a factor of 4 (1/2^2). Understanding how ΔV is affected by changes in q and r_1 and r_2 is crucial for analyzing and predicting the behavior of electric fields and potentials.
The potential energy per unit charge at a given point in an electric field.
Electric Field Constant (k): The constant that relates the electric force between two charges to their distance, defined as $k = 8.99 \times 10^9 \ N\cdot m^2/C^2$.