What is the capacitance of the two metal spheres shown in FIGURE EX26.22?

검증된 단계별 안내

Step 1: Understand the concept of capacitance. Capacitance (C) is defined as the ratio of the charge (Q) on one conductor to the potential difference (ΔV) between the two conductors. The formula is:

C = \frac{Q}{ΔV}

Step 2: Identify the given values from the figure. The charge on one sphere is

20 \times 10 ⁻ 9

C (20 nC), and the potential difference between the spheres is

100

Step 3: Substitute the values into the capacitance formula. Using

C = \frac{Q}{ΔV}

, replace Q with

20 \times 10 ⁻ 9

C and ΔV with

100

Step 4: Perform the division to calculate the capacitance. Divide the charge by the potential difference:

\frac{20}{\times}

. This will give the capacitance in Farads (F).

Step 5: Interpret the result. The capacitance value obtained will be in Farads, which is the SI unit for capacitance. This value represents the ability of the two spheres to store charge per unit potential difference.

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주요 개념

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

Capacitance

Capacitance is the ability of a system to store electric charge per unit voltage. It is defined as the ratio of the charge (Q) stored on the conductors to the potential difference (V) between them, expressed as C = Q/V. In the case of two metal spheres, the capacitance can be calculated based on their charges and the potential difference between them.

Electric Potential Difference

Electric potential difference, or voltage (ΔV), is the work done per unit charge in moving a charge between two points in an electric field. It is a measure of the energy difference that drives the flow of electric charge. In this scenario, the potential difference of 100 V indicates the energy required to move a charge between the two spheres with opposite charges.

Charge Distribution

Charge distribution refers to how electric charge is spread over a conductor's surface. In the case of the two spheres, one has a positive charge of +20 nC and the other a negative charge of -20 nC. This distribution affects the electric field between the spheres and is crucial for calculating the capacitance, as it determines how much charge can be stored for a given potential difference.