Showing posts with label Electron. Show all posts
Showing posts with label Electron. Show all posts

Force on Current Carrying Conductor Fleming Left Hand Rule

We can find the magnetic field around a wire on the axial line of charge using the Biot-Servert’s law. We are not adding the derivation here and the expression is as shown in the figure.

Let us consider a point on the axial line at a particular distance and let us assume that we know the radius at any given point.



The expression for the magnetic field at any point can be expressed as shown in the diagram. If we are measuring it at the center of the circle, we need to equate the value to zero.


We can also find out the force acting basing on Biot-Servert’s law. We can find the magnetic field at any given point using this rule. We know that the magnetic induction is defined as the force experienced by a unit north pole when placed in a magnetic field.


Thus we can measure the force as the product of the pole strength and magnetic induction. As the field is small component, the force is also small component. To get the total force acting on the point, we need to integrate the given equation and we can get the total force as shown in the diagram below.


This force will be maximum when the point is perpendicular to the current carrying conductor. If  the angle is zero or 180 degree, the force will become zero as shown below.


To  find  the  direction of the force experienced  by  the current carrying conductor using Fleming Left hand rule. As per the law, if  fore finger  indicate the direction of the magnetic  field and central finger indicates  the direction  of the  current then the thumb  indicates the direction of the thrust or force experienced by the current carrying conductor.

We  can also measure the force acting on  a charge simply by defining  the current as the rate of charge. We can define as the cross product of velocity of the charge and the magnetic field and the product is multiplied  with the charge.


We can  define  the  unit of  magnetic  induction tesla basing  on the above derivation. The magnetic  field induction is the force experienced by the  conductor when a  unit charge passing through  a conductor with unit velocity  at right angle.



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Photo Electric Effect Experimental Observations

When a light of suitable frequency incident on a metal surface, electrons are emitted from the metal surface and these electrons are called photo electrons. The corresponding current is called photo electric current and the phenomena is called photo electric effect.

Photo electric effect is possible with any of the metal surface when the light of suitable frequency is allowed to incident on the metal surface. The incident frequency shall have a minimum value for this photo electric effect to happen and the minimum frequency is called the threshold frequency. When the incident frequency is more than threshold frequency, photo electric effect can happen.

We can express the threshold value even in terms of wavelength. Being frequency is reciprocal to wave length; threshold wavelength is the maximum wavelength of the light that is allowed to incident on a metal surface therefore photo electrons can be emitted. It means when the incident light is having a wavelength less than the threshold wavelength, photo electric effect is possible.

To observe the properties of photo electric effect , experimental arrangement is made as shown below. The apparatus consists of a discharge due with the cathode and anode. Light is allowed to incident on the cathode. The anode is further connected to a rheostat and then further to input a voltage.

When the incident frequency is more than threshold frequency, from the cathode photo electrons are emitted and the emitted photo electric current is measured with the ammeter connected in the circuit.

It is noticed that the photo electric effect is instantaneous process. It means immediately after the striking of light, photo electrons are emitted. There is no time lag in between .

When the voltage is not applied, the photo electrons are not having enough energy to continue travelling in the circuit and to make a consistent current. The applied voltage is enabling the flow of the current through the circuit.

When no voltage is applied, the released electrons get struck between the cathode and anode and they are called stacked electrons. These electrons further oppose the flow of the current and to overcome it, we need to apply the voltage. With the applied voltage, we can notice a steady flow of current in the circuit.



It is experimentally observed that, with the increase of intensity of light, the corresponding photo electric current is also increasing. The graph drawn between intensity of the light in the photo electric current is a straight line passing through the origin.

When the positive plate of the battery is connected to the anode and the negative plate is connected to cathode, there is an increase in the photo electric current. If reverse voltage is applied to the cathode, that is connecting a positive plate to the cathode, it is practically noticed that with the increase of voltage, photo electric current starts decreasing.

At a particular reverse voltage, photo electric current becomes zero and this particular voltage is called stopping potential. At the stopping potential the kinetic energy of the electrons is compensated by the potential energy acquired by the electron due to the stopping potential. We can equate both the energies basing on the law conservation of energy.

It is also practically noticed that stopping potential is independent of intensity of light. With different intensity of light, there may be different photo electric currents. But for all the intensities, stopping potentially is same. It is represented on the negative x-axis of the graph. On this graph voltage is taken on x-axis and the photo electric current is taken and y-axis.



It is also practically noticed that, stopping potentially is a dependent of frequency of the incident light. It is noticeable that for different frequencies of incident light, the corresponding stopping potentially is different. It is also experimentally observed that change of the frequency of the incident light is not going to affect the saturation current that is generated.

It is experimentally observed that higher the incident frequency, more the stopping potential.



We can draw a graph taking the incident frequency on x-axis and the stopping potential on y-axis. The graph is as shown below. It is observed that the incident frequency shall be more than threshold frequency for the photo electric current to emit. Then only we can apply reverse voltage so that somewhere in the photo electric current stops. Once if the applied frequency is more than the threshold frequency, it is observed that with the increase of frequency, the stopping potential also increases.





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Millikan Oil Drop Method to determine Charge of Electron

We can calculate the charge on the electron basing on Millikan’s oil drop experiment. Between the two circular identical plates oil drops are sprinkled through a device called atomizer. The purpose of this device is to produce very small oil drops.

On the oil drop there are multiple forces acting. Weight is the force that is always acting in the downward direction, up thrust is the force that always acts in the upward direction. When the drop starts moving, there is another force called viscous force starts acting against the motion.

Viscous force is similar to frictional force which opposes the relative motion. As the drop starts moving in the downward direction, viscous force also increases in the upward direction. Being the downward force is constant and the upward force is steadily increasing, at a particular stage these two forces are going to be balanced with each other. At that instant the drop acquires a constant velocity and the velocity is called as terminal velocity.

The oil drops during the motion acquires a positive charge due to friction. If a electric field is applied in the upward direction, the drops starts experiencing a new electric force in the upward direction.

Again at the equilibrium state, the drop will acquire a different terminal velocity and by combining both the cases we can derive the equation for the charge.




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Determination of Specific Charge of Electron J J Thomson Experiment

The entire subject of physics can be broadly divided into two categories like classical physics and the modern physics. Classical physics deals with the macroscopic objects which moves with the velocity that is very much smaller than the velocity of light. Modern physics deals with objects which are microscopic in nature and moves with the velocity comparable to the velocity of light.

As per the concepts of modern physics, both radiation and matter has dual nature. The travel like a wave and it interacts like a particle. Discovery of the cathode rays is one of the important starting points of modern physics.

In a discharge tube if a very low pressure of 0.01 mm of Hg and a high voltage of 10,000 V is applied, invisible cathode rays are generated. These rays are invisible and they start from the cathode. They are nothing but stream of electrons which travel in straight lines with high velocity which is equal to 1 by 10th of velocity of light.

As they are having some velocity, they possess kinetic energy. They effect photographic plates and they can ionize the gases. As they are having a negative charge, they are affected by both electric and magnetic fields. The cathode rays are independent of the medium that is present in the discharge tube.

We can determine the specific charge of the cathode rays using JJ Thomson experiment. The apparatus consists of a discharge tube where a low pressure and high voltage is applied. There is a provision to apply electric and magnetic fields perpendicular to each other within the discharge tube. The cathode rays are allowed to strike a surface made up of zinc surface. When the invisible cathode Ray strikes the surface, there will be scintillation formed on the screen. Basing on the location of the scintillation we can identify the path of the cathode ray .

When no electric and magnetic fields are applied, cathode Ray travels along a straight line and strikes the screen exactly on the middle of the screen. When electric field is applied, there is a force acting on the cathode is therefore they were attracted towards the positive plate of the battery and hence modify their path.

When only magnetic field is applied perpendicular to previous electric field, the cathode Ray takes circular path. If both electric and magnetic fields are applied simultaneously in such a way that they apply equal force on the cathode ray, the cathode Ray goes in a undeviated manner.



We can derive the equations for specific charge basing on the equations of force experienced by the charged particle when electric field alone is applied and one magnetic field alone is applied.

When both the fields are applied perpendicular to each other, and if they are magnitudes are equal in size, the cathode Ray goes in a undeviated manner. It means that the cathode ray electron is in equilibrium position and hence we can equate both the forces.

When the cathode Ray is released, it is because of the high-voltage that is applied. Hence it will acquire some potential energy and by the time the cathode ray reaches the screen, all this potential energy is converted into kinetic energy. By applying the law of conservation of energy we can equate both these energies and derive an equation further for specific charge as shown below.




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