/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 We've seen that bees develop a p... [FREE SOLUTION] | 91Ó°ÊÓ

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We've seen that bees develop a positive charge as they fly through the air. When a bee lands on a flower, charge is transferred, and an opposite charge is induced in the earth below the flower. The flower and the ground together make a capacitor; a typical value is 0.80 pF. If a flower is charged to \(30 \mathrm{V}\) relative to the ground, a bee can reliably detect the added charge and then avoids the flower in favor of flowers that have not been recently visited. Approximately how much charge must a bee transfer to the flower to create a \(30 \mathrm{V}\) potential difference?

Short Answer

Expert verified
The charge a bee must transfer to the flower to create a \(30 \mathrm{V}\) potential difference is approximately \(24\) pC.

Step by step solution

01

Set up the relation between charge, voltage and capacitance

We have the relation between charge (Q), voltage (V) and capacitance (C) in a capacitor, which is \(Q = CV\). The charge we are trying to find out is the charge transferred by the bee to the flower.
02

Insert known values into the equation

The capacitance value is given as \(0.80\) pF (picoFarads) or \(0.80 \times 10^{-12}\) F (Farads) and the voltage difference is \(30 \mathrm{V}\). Now we can insert these values into our equation \(Q = CV\) to get \(Q = 0.80 \times 10^{-12} \mathrm{F} \times 30 \mathrm{V}\).
03

Calculate the charge transferred

By multiplying these numbers, we can get the charge transferred in Coulombs. So, \(Q = 0.80 \times 10^{-12} \mathrm{F} \times 30 \mathrm{V} = 24 \times 10^{-12}\) Coulombs or \(24\) pC (picoCoulombs).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Charge (Q)
Charge, symbolized by the uppercase letter 'Q', is a fundamental physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative. Like charges repel each other, while opposite charges attract.

In the context of the provided exercise, we can think of the bee as carrying an electric charge which it transfers to the flower upon landing. This is analogous to adding extra electrons (the carriers of negative charge) or removing them (which leaves behind a positive charge), resulting in a net charge on the flower. The amount of charge is measured in Coulombs (C), which is the standard unit of electric charge. However, for very small values, such as in our exercise, we use submultiples like the picoCoulomb (pC), where 1 pC is equal to 0.000000000001 Coulombs or 1x10^-12 C.

The process of charging the flower changes the electrical potential of the flower with respect to the ground and this potential difference can be detected by the bee, guiding its behavior.
Voltage (V)
Voltage, denoted by the letter 'V', is the measure of electric potential difference between two points in an electric field. The unit of voltage is volts (V). You can think of voltage as the electrical pressure that pushes electric charges through a conducting loop. It's the push that motivates charges to move.

In our problem, voltage is the potential difference that has been created between the flower and the earth when the bee transfers charge to the flower. A voltage of 30 V indicates that the electric potential of the flower has been raised, relative to the ground. This voltage can be compared to a height difference in a gravitational field: just as a ball will roll from a higher to a lower height because of a difference in gravitational potential, charges will move between points of different electric potentials due to voltage.

It's important to understand that voltage does not exist on its own but always as a difference between two points. In this case, it's the potential difference between the charged flower and the earth.
Capacitance (C)
Capacitance, symbolized by 'C', refers to the ability of a system to store charge per unit of voltage. It is measured in farads (F), named after the English scientist Michael Faraday. In practical electronics, farads are often too large to be useful, so we commonly see values in microfarads (μF), nanofarads (nF), or picofarads (pF).

In our exercise example, the flower and the ground constitute the plates of a capacitor. A capacitor is a two-terminal electrical component used in various electronic devices to store energy in the form of an electric field.

The specified capacitance of the flower-ground system is 0.80 pF. A capacitance of 0.80 pF is very small, reflecting the limited ability of this natural system to store charge. The relationship between voltage, charge, and capacitance in a capacitor is given by the equation Q = CV. When a charge is transferred onto the flower (as in the case of the bee), the amount of charge stored is directly proportional to the capacitance and the applied voltage. Therefore, for a constant capacitance, the charge on the capacitor will increase as the voltage increases.

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Most popular questions from this chapter

Guiana dolphins are one of the few mammals able to detect electric fields. In a test of sensitivity, a dolphin was exposed to the variable electric field from a pair of charged electrodes. The magnitude of the electric field near the sensory organs was measured by detecting the potential difference between two measurement electrodes located \(1.0 \mathrm{cm}\) apart along the field lines. The dolphin could reliably detect a field that produced a potential difference of \(0.50 \mathrm{mV}\) between these two electrodes. What is the corresponding electric field strength?

Under typical atmospheric conditions, there is an electric field near the earth's surface, directed downward, with a magnitude of \(100 \mathrm{V} / \mathrm{m}\). If we say that the potential at the earth's surface is \(0 \mathrm{V},\) what is the potential \(1.0 \mathrm{km}\) above the surface?

An electron with an initial speed of \(500,000 \mathrm{m} / \mathrm{s}\) is brought to rest by an electric field. a. Did the electron move into a region of higher potential or lower potential? b. What was the potential difference that stopped the electron? c. What was the initial kinetic energy of the electron, in electron volts?

At one point in space, the electric potential energy of a \(15 \mathrm{nC}\) charge is \(45 \mu \mathrm{J}\) a. What is the electric potential at this point? b. If a \(25 \mathrm{nC}\) charge were placed at this point, what would its electric potential energy be?

Two \(2.0 \mathrm{cm} \times 2.0 \mathrm{cm}\) square aluminum electrodes, spaced \(0.50 \mathrm{mm}\) apart, are connected to a \(100 \mathrm{V}\) battery. a. What is the capacitance? b. What is the charge on the positive electrode?

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