A −2.0 V equipotential surface and a +2.0 V equipotential surface are 1.0 mm apart. What is the electric field strength at a point halfway between the two surfaces?

Verified step by step guidance

1. Understand the relationship between electric field strength and potential difference. The electric field strength (E) is given by the formula: $E=\frac{\mathrm{\Delta V}}{d}$, where ΔV is the potential difference and d is the distance between the equipotential surfaces.
2. Determine the potential difference (ΔV) between the two surfaces. Since one surface is at −2.0 V and the other is at +2.0 V, the total potential difference is: $\mathrm{\Delta V}=\left|\right(+2.0)-(-2.0\left)\right|$.
3. Identify the distance (d) between the two surfaces. The problem states that the surfaces are 1.0 mm apart. Convert this distance to meters for consistency in SI units: $d=1.0\times 10⁻3m$.
4. Substitute the values for ΔV and d into the formula for electric field strength: $E=\frac{\mathrm{\Delta V}}{d}$. This will give the magnitude of the electric field strength.
5. Since the point of interest is halfway between the two surfaces, the electric field strength remains uniform between equipotential surfaces. The direction of the field will point from the positive surface (+2.0 V) to the negative surface (−2.0 V), as electric fields point from higher to lower potential.

Key Concepts

Equipotential Surfaces

Equipotential surfaces are regions in an electric field where the electric potential is constant. No work is done when moving a charge along an equipotential surface, as the potential difference is zero. In this question, the -2.0 V and +2.0 V surfaces indicate areas of differing electric potential, which are crucial for understanding the electric field's behavior between them.

Electric Field Strength

Electric field strength (E) is defined as the force (F) experienced by a unit positive charge (q) placed in the field, expressed as E = F/q. It can also be calculated from the potential difference (V) across two points and the distance (d) between them using the formula E = ΔV/d. This concept is essential for determining the electric field strength between the given equipotential surfaces.

Potential Difference

Potential difference, or voltage (ΔV), is the difference in electric potential between two points in an electric field. It is a measure of the work done per unit charge in moving a charge between those points. In this scenario, the potential difference between the -2.0 V and +2.0 V surfaces is 4.0 V, which is critical for calculating the electric field strength at the midpoint.