Ch 26: Potential and Field

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 26: Potential and Field

Problem 22

Chapter 26, Problem 22

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

Verified step by step guidance

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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Key Concepts

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

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.

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Related Practice

Textbook Question

Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery. What is the capacitance?

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Textbook Question

Light from the sun allows a solar cell to move electrons from the positive to the negative terminal, doing 2.4×10⁻¹⁹ J of work per electron. What is the emf of this solar cell?

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Textbook Question

A 6 μF capacitor, a 10 μF capacitor, and a 16 μF capacitor are connected in series. What is their equivalent capacitance?

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Textbook Question

What is the equivalent capacitance of the three capacitors in FIGURE EX26.27?

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Textbook Question

A switch that connects a battery to a 10 μF capacitor is closed. Several seconds later you find that the capacitor plates are charged to ±30 μC. What is the emf of the battery?

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Textbook Question

Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery. What is the magnitude of the charge on each electrode?

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