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. V_O​>V_A
• B. V_O​<V_A​
• C. V_O​>V_B
• D. V_O​<V_B

Answer 1

The Correct Option is A

Given a uniform electric field E in the positive X-direction:

ΔV = -E·Δr

V_O vs V_A:

O(0,0), A(+2 cm,0)
Δr = 2 cm î
V_A - V_O = -E·2 cm < 0
⇒ V_O > V_A

V_O vs V_B:

• B(0,+1 cm)
Δr = 1 cm ĵ
V_B - V_O = -E·0 = 0
⇒ V_O = V_B

Only option (1) V_O > V_A is correct.

Thus, we have V_O​=V_B​ and V_O​\(>\)V_A​, which means the correct answer is (1).

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 V_O​=V_B​ and V_O​\(>\)V_A​, which means the correct answer is (1).