Question

Figure shows three points $A, B$ and $C$ in a region of uniform electric field $\vec{E}$ . The line $AB$ is perpendicular and $BC$ is parallel to the field lines. Then which of the following holds good? where $V_A, V_B$ and $V_C$ represent the electric potential at the points $A, B$ and $C$ respectively.

• A. $V_A = V_B = V_C$
• B. $V_A = V_B > V_C$
• C. $V_A = V_B < V_C$
• D. $V_A > V_B = V_C$

Answer 1

Answer: (B)

$V_A = V_B > V_C$

Answer 2

Key Idea : Electric lines of force flow from higher potential region to lower potential region. The electric field intensity of a point in an electric field in a given direction is equal to the negative potential gradient in that direction,
i.e.,
$E=-\frac{d V}{d x}$
The negative sign signifies that the potential decreases in the direction of electric field, i.e., electric lines of force flow from higher potential region to lower potential region.
Since, $A B$ is perpendicular to field lines, so $A$ and $B$ are at same potential.
Hence, $V_{A}=V_{B}>V_{C}$