Do you thin it is possible to have the benefits of the Agricultural and Industrial revolutions without the environmental costs?

A charge is divided q1 and (q-q1)what will be the ratio of q/q1 so that force between the two parts placed at a given distance i

Arturiano [62]

Answer:

$q / q_{1} = 2$ , assuming that $q_{1}$ and $(q - q_{1})$ are point charges.

Explanation:

Let $k$ denote the coulomb constant. Let $r$ denote the distance between the two point charges. In this question, neither $k$ and $r$ depend on the value of $q_{1}$ .

By Coulomb's Law, the magnitude of electrostatic force between $q_{1}$ and $(q - q_{1})$ would be:

$\begin{aligned}F &= \frac{k\, q_{1}\, (q - q_{1})}{r^{2}} \\ &= \frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\end{aligned}$ .

Find the first and second derivative of $F$ with respect to $q_{1}$ . (Note that $0 < q_{1} < q$ .)

First derivative:

$\begin{aligned}\frac{d}{d q_{1}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\right] \\ &= \frac{k}{r^{2}}\, \left[\frac{d}{d q_{1}} [q\, q_{1}] - \frac{d}{d q_{1}}[{q_{1}}^{2}]\right]\\ &= \frac{k}{r^{2}}\, (q - 2\, q_{1})\end{aligned}$ .

Second derivative:

$\begin{aligned}\frac{d^{2}}{{d q_{1}}^{2}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q - 2\, q_{1})\right] \\ &= \frac{(-2)\, k}{r^{2}}\end{aligned}$ .

The value of the coulomb constant $k$ is greater than $0$ . Thus, the value of the second derivative of $F$ with respect to $q_{1}$ would be negative for all real $r$ . $F\!$ would be convex over all $q_{1}$ .

By the convexity of $\! F$ with respect to $\! q_{1} \!$ , there would be a unique $q_{1}$ that globally maximizes $F$ . The first derivative of $F\!$ with respect to $q_{1}\!$ should be $0$ for that particular $\! q_{1}$ . In other words:

$\displaystyle \frac{k}{r^{2}}\, (q - 2\, q_{1}) = 0$ <em>.</em>

$2\, q_{1} = q$ .

$q_{1} = q / 2$ .

In other words, the force between the two point charges would be maximized when the charge is evenly split:

$\begin{aligned} \frac{q}{q_{1}} &= \frac{q}{q / 2} = 2\end{aligned}$ .

3 0

3 years ago

What is the value of acceleration due to gravity, g, on Earth?

qwelly [4]

Explanation:

It varies with altitude, but at sea level, it's 9.8 m/s².

8 0

4 years ago

A quantitative description of kinematics involves using ___ th describe the motion

Semmy [17]

Answer:

numbers

Explanation:

Virtually all unimaginable processes can be described as the movement of certain objects. To analyze and predict the nature of the movements that result from the different kinds of interactions, some important concepts such as momentum, force and energy have been invented. If momentum, force, and energy are known and expressed in a quantitative way (that is, by numbers) it is possible to establish rules by which the resulting movements can be predicted.

4 0

3 years ago

Characteristics that a scientific measuring tool should have

bixtya [17]

Answer:

RELIBILITY - is the consistency of your measurement, or the degree to which an

instrument measures the same way each time it is used under the same condition with the

same subjects. In short, it is the repeatability of your measurement. A measure is considered

reliable if a person's score on the same test given twice is similar. It is important to

remember that reliability is not measured, it is estimated. A good instrument will produce

consistent scores. An instrument’s reliability is estimated using a correlation coefficient of

one type or another.

VALIDITY

VALIDITY - Validity is the extent to which a test measures what it claims to measure. It is

vital for a test to be valid in order for the results to be accurately applied and interpreted.

Validity isn’t determined by a single statistic, but by a body of research that demonstrates

the relationship between the test and the behavior it is intended to measure. There are three

types of validity: It is the strength of our conclusions, inferences or propositions. More

formally, Cook and Campbell (1979) define it as the "best available approximation to the

truth or falsity of a given inference, proposition or conclusion."

PRACTICIBILITY

PRACTICIBILITY - It should be feasible & usable. Quality of being usable in context to the

objective to be achieved.

USABILITY

USABILITY(practicality) ease in administration, scoring, interpretation and application, low

cost, proper mechanical make – up

MEASUREABILITY

MEASUREABILITY - It should measure the objective to be achieved.

Explanation:

5 0

2 years ago

According to the principle of faunal succession, what must be true of the fossils on a layer below? Now

Firdavs [7]

It means that they were set earlier therefor they are older.

7 0

3 years ago

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