Certain sharks can detect an electric field as weak as $1.0$ $μ$ V/m. To grasp how weak this field is, if you wanted to produce it between two parallel metal plates by connecting an ordinary $1.5$ V AA battery across these plates, how far apart would the plates have to be?

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Understand the relationship between electric field (E), voltage (V), and distance (d) between plates. The electric field between two parallel plates is given by the formula:

E = \frac{V}{d}

Identify the given values in the problem: the electric field (E) is 1.0 μV/m, which is equivalent to 1.0 x 10^-6 V/m, and the voltage (V) is 1.5 V.

Rearrange the formula to solve for the distance (d) between the plates:

d = \frac{V}{E}

Substitute the known values into the rearranged formula:

d = \frac{1.5}{1.0 	imes 10^{-6}}

Calculate the distance (d) using the substituted values to find how far apart the plates need to be to produce the electric field of 1.0 μV/m with a 1.5 V battery.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Electric Field

An electric field is a region around a charged object where other charged objects experience a force. It is represented by the symbol E and measured in volts per meter (V/m). The strength of the electric field is determined by the voltage applied and the distance between the plates, following the formula E = V/d.

Voltage

Voltage, or electric potential difference, is the measure of the energy per unit charge available to move electrons between two points. It is measured in volts (V) and is a key factor in determining the electric field between two plates. In this scenario, a 1.5 V AA battery provides the voltage needed to create the electric field.

Distance Between Plates

The distance between two parallel plates affects the strength of the electric field created between them. According to the formula E = V/d, the electric field (E) is inversely proportional to the distance (d). To achieve a weak electric field of 1.0 μV/m, the plates must be placed at a specific distance calculated using the given voltage.