Which point in FIGURE EX26.5, A or B, has a larger electric potential?

Verified step by step guidance

Step 1: Understand the relationship between electric potential and electric field. The electric potential decreases in the direction of the electric field. The formula for the change in electric potential is ΔV = -E * d, where E is the magnitude of the electric field and d is the distance moved in the direction of the field.

Step 2: Analyze the diagram. The electric field is uniform and directed horizontally to the right, with a magnitude of E = 1000 V/m. Points A and B are separated vertically by 3 cm and horizontally by 7 cm.

Step 3: Determine the relative positions of points A and B. Point A is higher vertically, while point B is lower and further to the right. Since the electric field is horizontal, the vertical separation does not affect the electric potential difference.

Step 4: Calculate the horizontal displacement between points A and B. The horizontal distance is 7 cm (0.07 m). Use the formula ΔV = -E * d to find the potential difference due to this displacement. Since point B is further to the right, it is in the direction of the electric field, meaning its potential is lower than point A.

Step 5: Conclude that point A has a larger electric potential than point B because the electric potential decreases in the direction of the electric field, and point B is further along the field direction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Potential

Electric potential, measured in volts, represents the potential energy per unit charge at a point in an electric field. It indicates how much work is needed to move a charge from a reference point to a specific point within the field. In this context, the electric potential at points A and B can be compared based on their positions relative to the electric field.

Electric Field

An electric field is a region around a charged object where other charged objects experience a force. It is represented by field lines, with the direction indicating the force on a positive charge. The strength of the electric field (E) is given in volts per meter (V/m) and affects the electric potential at different points within the field.

Relationship Between Electric Field and Potential

The relationship between electric field and electric potential is defined by the equation E = -dV/dx, where E is the electric field strength and dV/dx is the change in electric potential over distance. This means that in a uniform electric field, the potential decreases in the direction of the field. Thus, the point closer to the positive charge will have a higher electric potential.