Consider a point charge q=1.0 μC, point A at distance d1=2.0 m from q, and point B at distance

step 1 Over here we have given two different scenarios and we need to find the potential difference bet

Consider a point charge q=1.0 μC, point A at distance d1=2.0...

Consider a point charge $q=1.0 \mu \mathrm{C}$, point $A$ at distance $d_{1}=2.0 \mathrm{~m}$ from $q$, and point $B$ at distance $d_{2}=$ $1.0 \mathrm{~m} .$ (a) If these points are diametrically opposite each other, as in Fig. $25-28 a$, what is the electric potential difference $V_{A}-V_{B} ?$ (b) What is that electric potential difference if points $A$ and $B$ are located as in Fig. $25-28 b ?$

Consider a point charge $q=1.0 \mu \mathrm{C}$, point $A$ at distance $d_{1}=2.0 \mathrm{~m}$ from $q$, and point $B$ at distance $d_{2}=$ $1.0 \mathrm{~m} .$ (a) If these points are diametrically opposite each other, as in Fig. $25-28 a$, what is the electric potential difference $V_{A}-V_{B} ?$
(b) What is that electric potential difference if points $A$ and $B$ are located as in Fig. $25-28 b ?$

Key Concepts

Distance Dependence in Electric Fields

The electric potential due to a point charge varies inversely with the distance from the charge (r), which means that small changes in distance can lead to significant changes in potential, especially near the charge. Understanding this inverse relationship is crucial when comparing potentials at different distances from a point charge.

Conservative Nature of Electrostatic Fields

In electrostatics, the electric field created by static charges is conservative, meaning that the work done (or potential difference) in moving a charge between two points is independent of the path taken. This property allows the use of potential functions to simplify the analysis of electric fields and potential differences in different geometrical configurations.

Electric Potential Due to a Point Charge

This concept describes the electric potential (voltage) at any point in space created by a point charge, given by the formula V = kq/r, where k is Coulomb’s constant, q is the charge, and r is the distance from the charge. It is fundamental for determining how the potential varies with distance and forms the basis for understanding potential in more complex charge configurations.

Electric Potential Difference

The electric potential difference between two points is the difference in electric potential (voltage) between those points, which represents the energy per unit charge required to move a test charge from one point to another. This concept is key to many electrostatic problems and is independent of the path taken in a conservative electric field.

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