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Sedaia [141]
4 years ago
14

To understand the nature of electric fields and how to draw field lines. Electric field lines are a tool used to visualize elect

ric fields. A field line is drawn beginning at a positive charge and ending at a negative charge. Field lines may also appear from the edge of a picture or disappear at the edge of the picture. Such lines are said to begin or end at infinity. The field lines are directed so that the electric field at any point is tangent to the field line at that point.

Physics
1 answer:
Brrunno [24]4 years ago
7 0

Explanation:

The electric field is defined as the change in the properties of space caused by the existence of a positively (+) or negatively (-) charged particle. The electric field can be represented by infinitely many lines from a particle, and those lines never intersect each other. Depending on the type of charge we can see different cases:

  • Let's say we have a <u>positive charge alone (</u>image 1)<u>.</u> The field lines are drawn from the centre of the particle outwards to infinity (in other words, they disappear from the edge of the picture). Meaning the direction of the electric field points outwards the particle.
  • For a <u>negative charge alone </u>(image 2)<u>,</u> the lines come from infinity to the centre, and point towards the particle (i.e. lines appear from the edge of the picture).

Let's see what happens if we have two charges together:

  • <u>Two positive charges</u> (image 3): Since the charges are of the same type (positive), the particles repel each other. Then the field lines will avoid each other so they do not join. The charge is positive, so lines point outwards.
  • <u>Two negative charges</u> (image 4): Again, the charges are both negative, so they repel. But they are negative, so the field points inwards.
  • <u>Negative and positive charges</u> (image 5): They are different charges, so the force between them is attractive. This causes the field lines from both to join. They go out of the positive and come into the negative particle.

Image 6:

The lines are passing through infinite points of the space. If we choose a certain point and measure the electric field, we can see to which direction the electric field points. This is the direction of the electric field vector. It does not matter which point we choose; the electric field vector touches the field line only at this point, which means it is tangent to the field line.

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nordsb [41]

A) 320 count/min

B) 40 count/min

C) 80 count/min, 11400 years

Explanation:

A)

The activity of a radioactive sample is the number of decays per second in the sample.

The activity of a sample is therefore directly proportional to the number of nuclei in the sample:

A\propto N

where A is the activity and N the number of nuclei.

As a consequence, since the number of nuclei is proportional to the mass of the sample, the activity is also directly proportional to the mass of the sample:

A\propto m

where m is the mass of the sample.

In this problem:

- When the mass is m_1 = 1 g, the activity is A_1=16 count/min

- When the mass is m_2=20 g, the activity is A_2

So we can find A2 by using the rule of three:

\frac{A_1}{m_1}=\frac{A_2}{m_2}\\A_2=A_1 \frac{m_2}{m_1}=(16)\frac{20}{1}=320 count/min

B)

The equation describing the activity of a radioactive sample as a function of time is:

A(t)= A_0 e^{-\lambda t} (1)

where

A_0 is the initial activity at time t = 0

t is the time

\lambda is the decay constant, which gives the probability of decay

The decay constant can be found using the equation

\lambda = \frac{ln2}{t_{1/2}}

where t_{1/2} is the half-life, which is the amount of time it takes for the radioactive sample to halve its activity.

In this problem, carbon-14 has half-life of

t_{1/2}=5700 y

So its decay constant is

\lambda=\frac{ln2}{5700}=1.22\cdot 10^{-4} y^{-1}

We also know that the tree died

t = 17,100 years ago

and that the initial activity was

A_0 = 320 count/min (value calculated in part A, corresponding to a mass of 20 g)

So, substituting into eq(1), we find the new activity:

A(17,100) = (320)e^{-(1.22\cdot 10^{-4})(17,100)}=40 count/min

C)

We know that a sample of living wood has an activity of

A=16 count/min per 1 g of mass.

Here we have 5 g of mass, therefore the activity of the sample when it was living was:

A_0 = A\cdot 5 = (16)(5)=80 count/min

Moreover, here we have a sample of 5 g, with current activity of A=20 count/min: it means that its activity per gram of mass is

A'=\frac{20}{5}=4 count/min

We know that the activity halves after every half-life: Here the activity has became 1/4 of the original value, this means that 2 half-lives have passed, because:

- After 1 half-life, the activity drops from 16 count/min to 8 count/min

- After 2 half-lives, the activity dropd to 4 count/min

So the age of the wood is equal to 2 half-lives, which is:

t=2t_{1/2}=2(5700)=11,400 y

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