Question

A uniform electric field pointing in the positive X direction exists in a region. Let O be the origin, A be the point on the X-axis at r = +2 cm, and B be the point on the Y-axis at y = +1 cm. Then the potential at the points O, A, and B satisfy:

• A. VO​>VA
• B. VO​<VA​
• C. VO​>VB
• D. VO​<VB

Answer 1

Answer: (A)

VO​>VA

Answer 2

The electric potential decreases in the direction of the electric field. Since the electric field points along the positive X direction, it means that as you move in this direction, the potential decreases.
Point O is at the origin, so it’s the reference point. Point A is along the X-axis at r=+2 cm, which is in the direction of the field. Therefore, the potential at A will be lower than at O. Point B is along the Y-axis at y=+1 cm. Since there is no component of the electric field along the Y-axis, no work is done in moving a charge from O to B. Hence, the potential at B is the same as at O.
Thus, we have VO​=VB​ and VO​$>$VA​, which means the correct answer is (1).