(II) A uniform electric field E→ = -6.30 N/Cî points in the negative x direction as shown in Fig. 23–40. The x and y coordinates of points A, B, and C are given on the diagram (in meters). Determine the differences in potential
(a) V_BA , 
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Verified step by step guidance

1. Identify the coordinates of points A and B from the diagram. Let's denote them as (x_A, y_A) for point A and (x_B, y_B) for point B.
2. Understand that the electric potential difference between two points in an electric field is given by the negative of the integral of the electric field along the path from one point to the other. The formula can be expressed as V_B - V_A = - \int_{A}^{B} \vec{E} \cdot d\vec{l}.
3. Since the electric field is uniform and only in the x-direction, the potential difference only depends on the x-coordinates of points A and B. Simplify the integral to V_B - V_A = -E (x_B - x_A), where E is the magnitude of the electric field.
4. Substitute the values of E, x_A, and x_B into the equation. Remember that E is given as -6.30 N/C, which indicates the direction of the field is negative along the x-axis.
5. Calculate the potential difference V_BA by finding the difference V_B - V_A using the values substituted in the previous step. This will give you the potential difference from point B to point A in the electric field.

Key Concepts

Electric Field

An electric field is a region around a charged particle where other charged particles experience a force. It is represented by the symbol E and is measured in newtons per coulomb (N/C). The direction of the electric field is defined as the direction a positive test charge would move, which in this case is in the negative x direction.

Electric Potential Difference

Electric potential difference, or voltage (V), is the work done per unit charge in moving a charge between two points in an electric field. It is calculated as the negative integral of the electric field along a path between the two points. In this context, V_BA represents the potential difference between points B and A, which can be determined using the electric field and the distance between these points.

Coordinate System

A coordinate system is a method for identifying the position of points in space using numerical values. In this problem, the x and y coordinates of points A, B, and C are essential for calculating the potential difference. Understanding how to interpret these coordinates in relation to the electric field allows for accurate calculations of potential differences between the specified points.