Saturday, July 2, 2011

Ampere's Circuital Law Problem





A linear set of wires is given to you. The current in the wires is flowing perpendicular to the plane of paper and towards the reader. The set is infinitely long and the current flowing through the set is uniform and that is lambda amperes per unit width.We have to find out the magnetic field due to this current distribution.



We'll solve this problem by using Ampere's circuital law.

Since, current distribution is uniform, w can create a closed surface for any amount of width.

So, ABCD is the rectangular ampere's closed surface which has a width x. We'll do the calculation with respect to this closed surface. In the diagram, I have shown you the direction of magnetic field B. I found the direction using Fleming's Right Hand Rule. According to this rule, we have to place the thumb along the direction of current, then we have to open our palm and make a pushing movement. The direction along which the palm seems to knock will be the direction of magnetic field.

Now we are going to apply the Ampere's Circuital Law.




In 2 cases, B and dl are parallel to each other. So angle between them is 0 deg. Therefore cos 0 = 1.
In the other 2 cases, B and dl are perpendicular to each other. So angle between them is 90 deg. cos 90 = 0.

Therefore, out of the 4 results, 2 of them are not considered as they are equal to 0.




So, solved.

Friday, July 1, 2011

Physiologically dry soil

Physiologically dry soil is that kind of soil in which, concentration of salts are very high. That's why halophytes grow in that kind of soil. It is found in Sunderbans area, India.

Thursday, June 30, 2011

Ecology question set 1

You have an ecosystem with the following organisms: birds, fruit trees, tigers, and monkeys. Which list would best describe the food chain?
tigers, monkeys, birds, fruit trees
birds, fruit trees, monkeys, tigers
fruit trees, birds, tigers, monkeys
fruit trees, birds/monkeys, tigers

Food chains and webs not only describe the order in which organisms are eaten, but they also describe the _____.
flow of energy in an ecosystem
importance of the ecosystem
health of the ecosystem
animals that are all related

In the food chain, ____ can make their own food.
producers
primary consumers
secondary consumers
decomposers



--------


Answers:


Question 1


The food chain would move like this:


producer --> primary consumers--> secondary consumers---> tertiary consumers --> final consumers.


In the first question producer is definitely the fruit tree.
Here, birds/monkeys both are herbivores, therefore these are primary consumers.


Tigers are carnivorous. so, tigers belong to the  category secondary consumers. 


Therefore the first answer is: fruit trees, birds/monkeys, tigers


Question 2


Well, what food chain means is given partially in the question. But the idea behind food chain and food web is to represent the directional sequence in which energy flows from one species to the next. 


Therefore the correct answer is flow of energy in an ecosystem.


Question 3


producers fix a little fraction of the energy that they receive from the sun. This energy is fixed into chemical energy(food).


Correct option: producers

What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle?

What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle?

A point charge q = 5.0 ┬ÁC is placed at each corner of an equilateral triangle with sides 0.20m in length.
A) What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle?
B) Is the magnitude of the electric field at the center of the triangle greater than, less than, or the same as the magnitude at the midpoint of a side? Explain.
please help me please.

Answer:





I have arranged the charges as above at the three vertices of equilateral triangle.


so according to the diagram, at any side of the triangle, fields of two charges will neutralize each other. So, only the field due to one remaining charge will be the net electric field.




In the above diagram, the red vector and the black vector neutralizes each other. So, only the violet vector remains.




So, the net electric field will be due to one charge only.

But, at the centre, all the field vectors from the individual charges will act. According to the diagram, they make an angle of 120 deg with each other. So, the net force becomes zero.

Arc and infinite wire problem 1

The question:

The field at the centre O of a semi circular wire of radius r(see fig.) if the straight wires are of infinite length is:-



Options


ANSWER

The net field at point O is = field due to the straight wires + field due to the arc



first we'll try to understand the straight line case: 

We'll divide it into two separate discussions 

1> Magnitude
2> direction





In the above case the formula we use for finding out the magnetic field at a particular point at space is given by:

Here d is the perpendicular distance from the mid point of wire to the point concerned.

But, the situation given in the question is a modification of the above situation.





In the above diagram,
The arrow on the black wire shows the direction of current.
The red arrow from the black wire heads towards the point at which we have to find the magnetic field.
Therefore the red line is r.
And the point is O. I forgot to show it in the diagram.
Kindly note.

So we'll solve the straight lines part first:

Using Fleming's rule or right hand palm rule, we know that for both the wires, the magnetic field is in the same direction, so we find the field due to one and multiply it by 2.



The above Field is towards the observer.

The magnetic field due to a current carrying circular loop is given by:



So the formula to find the magnetic field due to the arc:


Here alpha radian is the angle subtended by the arc.

Here alpha = pi.

Therefore,

the Magnetic field due to the arc is:


Now subtract the magnetic field due to straight lines from the magnetic field due to arc.


Tuesday, June 28, 2011

Which of the following are global environmental problems? Why?


Which of the following are global environmental problems? Why?

a.The growth of human population
b.The furbish lousewort, a small flowering plant found in the state of Maine.It is so rare that it has been seen by few people and is considered endangered
c.The blue whale, listed as an endangered species under the us marine mammal protection act.
d.A car that has air conditioning
e.seriously polluted harbors and coastlines in major ocean ports


My answer:


a,d, e are environmental problems


The growth of human population


REduction of natural resources
deforestation to build homes
pollution


A car that has air conditioning


CFC released by it causes disruption of ozone layer.


seriously polluted harbors and coastlines in major ocean ports


Bacterias grow on the pollutant, reduces the oxygen level of water. Disrupt the aquatic ecosystem.


Question found at:

Physics tension question wires help

Question asked:



Sorry I can't copy the image on here so I put a link at the bottom of the page.
A picture with mass of 22.5 kg is supported by two wires. Find the tension in each cable.

When the picture is hanging from the wire, the wire makes an uneven V shape. The left part of the wire is T2 (tension 2) and the right wire is T1. The angle that the left wire makes with the ceiling is 60 degrees and the right wire makes a 30 degree angle as seen below.


How to I find the tension in each cable??


MY ANSWER:

Just take a look at the diagram.

Just take a look at the diagram.

Forces along y direction balances each other.

T1 sin 30 + T2 sin 60 = mg ------- (1)

Forces along x direction balances each other

T1 cos 30 = T2 cos 60 --- 2

Solving equation 2 we get:

T2 = T1 * root(3)

Substituting the value of T2 in equation 1 we get:

T1/2 + 3T1/2 = 22.5 * g

I take g as 10m/s^2

So solving I get, T1 = 112.5 N

Substituting the value of T1 in equation 2, we get

22.5 *5* root(3)/2 = T2/2

SOlving we get, T2 = 194. 85 N.

Hope this helps






QUESTION answered by Mr Idecide