Electric and Magnetic Fields

  • We will now discuss electric and magnetic field vectors (E and B)at a point in the absence of charge.
  • Now let us place a charge q at point (x,y,z) in space. If this charge experiences a force as given by Lorentz force equation then we can associate vectors E and B with this point (x,y,z) in space.
  • Thus at any time t vectors E(x,y,z,t) and B(x,y,z,t) gives forces experienced by any charge q at point (x,y,z) with a condition that placing this charge at point (x,y,z) in space does not disturb the position or motion of all other charges responsible for the generation of the field.
  • So, every point in space is associated with vector E and B which are functions of x,y,z and t.
  • Since E(or B) can be specified at every point in space , we call it a field.
  • A field is that physicsl quantity which takes on different values at different points in space for example velocity field of a flowing liquid.
  • Electromagnetic fields as we know are produced by complex formulas but the relationships between values of the fields at one point and the values of the feld at neighbour points are vary simple and can form differential equations which can completely describe the field.
  • To understand and visualize the behaviour of field we can consider the field as a function of position and
  • time. We can also create a mental picture of field by drawing the vectors at many points in space each of which gives strength and direction of field at that point.
  • Flux is one property of field and flux of a vector field through a surface is defined as the average value of normal component of the vector times the area of the surface.
  • Another property is the circulation of the vector field and for any vector field circulation around any imagined closed curve is defined as the average tangential component of the vector multiplied by the circumfrance of the loop.
  • With just the idea of flux and circulation we can define all the laws of electricity and magnetism.
Refrence:- The Feynman lectures on physics Vol 2

Galilean Transformation

Motion is a relative concept . You are sitting on a train. A object on trains seems to be at rest from your perspective but it is in motion from the person standing on the ground.So it is tied to particular frame of refrence choosen by observer.
Now Different observer may use different frame of refrence , And velocity ,acceleration may be different from these different frame of refrence
It is important to know how these measurement in different frame of refrence are related.
For two observer S1 and S2 who move relative to each other with rectilinear motion, The velocity,displacement and acceleration of an object measured from these two observer are related as
r2=r1 -R
Where r1 is the position vector of object from observer S1 and r2 is the position vector of object from observer S2. R is the position of observer S2 from S1
v2=v1 -v
Where v1 is the velocity of object relative to observer S1 and v2 is the velocity of object relative to observer S2. v is the velocity S2 relative to S1
a2=a1 -a
Where a1 is the acceleration of object relative to observer S1 and a2 is the acceleration of object relative to observer S2. a is the acceleration S2relative to S1
When the two observer are moving in uniform relative translation motion with velocity v and t=0 when the observer were coincident,these equation becomes
r2=r1 -vt
v2=v1 -v
The above equation are called Galilean transformation of coordinates ,velocities and accelerations
So acceleration of the object remains same for all observer in uniform relative translational motion

Law of Radioactive decay

  • Radioactivity is a nuclear phenomenon
  • When a nucleus disintegrates by emitting a particle ( α and β) or by capturing an electron from the atomic shell( K-shell) ,the process is called radioactive decay. This decay process is spontaneous.
  • Let us take a radioactive sample containing N0 at time t=0 i.e, at the beginning. We wish to calculate the number N of these nuclei left after time t.
  • The number of nuclei of a given radioactive sample disintegrating per sec is called the activity of that sample is
    dN/dt=rate of decrease of nuclei with time=Activity of sample at time t                              --(1)
  • Experimentally it is found that the activity at any instant of time t is directly proportional to the number N of parent type nuclei present at that time

    Where λ > 0 is proportionality constant and negative sign indicates that N decreases as t increases
  • From equation (2) we get

    i.e. ,λ is fractional change in N per sec
    => λ is not merely a proportionality constant ,but it gives us the probability of decay per unit interval of time
  • Hence λ is called the probability constant or decay constant or disintegration constant
  • dN is the no of parent nuclei that decay between t and t+dt and we have taken N as continuous variable 
  • From (2)

    N0=No of radioactive nuclei at t=0
  • From (4) we see that law of radioactive decay is exponential in character

  • From figure it can be noted that only half the amount of radon present initially after 3.83 days and 1/4 after 7.66 days and so on
  • Plot shows that in a fixed time interval a fixed fraction of the amount of radioactive substance at the beginning of interval decays
  • This faction is independent of the amount of radioactive substance and depends only on the interval of the time
  • The decay constant λ is a characteristics of radioactive substance and it depends in no way on the amount of the substance present

Popular Posts