Showing posts with label Electric Charge. Show all posts
Showing posts with label Electric Charge. Show all posts

Electric Intensity and Torque due to Electric Dipole Video Lesson

Electric dipole is the combination of two charges of equal magnitude but opposite nature separated by small distance.Electric intensity is the force experienced by a unit positive charge placed in the electric field of dipole. Torque is the turning experience got by a electric dipole when placed in an external electric field.

 Electric Field intensity on the axial line of dipole

A line passing through two charges is called axial line. We would like to measure the electric field intensity at any point on the axial line of electric dipole. Let us consider a point on the axial line at a distance r from the center of the dipole. We shall imagine a unit positive charge at the considered point. It experience force both due to positive and negative charge. Due to Positive charge force is repulsive and due to negative charge it is attractive. Using Coulomb's inverse square law, we need to write equations  for the force experienced by unit positive charge at the given location.We need to measure the effective force as the difference between the two charges and it can be further simplified as shown in the video lesson below. Electric dipole moment is the product of any one charge of the dipole to the distance between the two charges of dipole. It is a vector quantity and its direction is from negative charge towards positive charge. Intensity is expressed in terms of dipole moment as shown below.



Electric field intensity on equatorial line of Dipole

Equatorial line is a line passing through the center of dipole and perpendicular to the axial line. Let us consider a point on that line that is at a finite distance  from center of dipole. We shall imagine a unit positive charge at that point and it experience force due to both positive and negative charge of the dipole. Its magnitude can be determined using inverse square law and its value is shown in the video below. The force due to positive charge is repulsive on unit positive charge and force due to negative charge is attractive. Their directions were identified and the resultant is determined using the vector laws of addition as  shown in the video lesson below. It can be noticed that the electric intensity on the equatorial line is half that of intensity on the axial line. A detailed proof is given in the video lesson below. Its direction is also shown.



Electric Intensity at any point on the dipole

Let us consider a point around the dipole that is neither on the axial line or equatorial line and the point is at a distance and is making some angle with the horizontal line. To find the electric field intensity at that point, we can consider the dipole as the combination of two dipoles that are perpendicular to each other as shown in the video lesson. For one dipole the considered point is on the axial line and for the other imagined dipole the point is on the equatorial line. As we have derived the equations for the intensity on axial line and equatorial line, we can use that equations and they two are perpendicular to each other. By simplifying them further as shown in the video lesson, we can get the resultant equation as shown. This is a generic equation and in that equation, if the angle is zero, the point will be on axial line and if the angle is ninety degree, the point goes to equatorial line. 


Torque experienced by dipole when placed in a uniform electric field

Let us consider a dipole of two charges separated by a small distance and let us apply a electric field of known intensity on it. Each charge experience a force and and the two forces are equal in magnitude but opposite in direction. But they don't cancel each other as the two forces are acting on different points of the electric dipole. Thus it experience a turning effect in anti clock wise direction and we can measure the torque as shown in the video lesson below. Torque is defined as the product of any one force and the perpendicular distance between the two forces acting on the dipole. It is a vector and we can find the direction using the right hand thumb rule or cork screw rule as shown in the video lesson below.



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Neutral Point and Equilibrium of Electric charge in a line Video Lesson

Electrically  neutral point is a location at which the resultant electric force is zero. It means the charge kept at that point is experiencing equal and opposite force due to the other two charges kept in that line. To find the neutral point, we can equate the two forces and when the two charges are of similar nature, we can get null point between the charges existing in one line and beyond them, we are not going to find the neutral point. At a location beyond the neutral point, the force acting on the third charge are in the same direction and hence there will  not be any neutral point. It is explained in the following video lesson and the location of neutral point is also derived.



Neutral Point between opposite charges

When the charges are of opposite nature, the resultant force on a third charge in between them is not zero and it is experiencing the two force in the same directions. If we consider a location out side the two charges and consider a third charge, it experience forces due to two charges in opposite direction. If they are equal in magnitude, we can get null point as shown in the video lesson. The expression for the location of null point is also derived here.


Equilibrium of system of three charges

Now we are considering a scenario of three charges kept on a straight line. If the two charges at the ends of the line, we can get null point between them weather we keep positive or negative charges in between them. But to keep any of the positive charge at the end of the system, we shall only keep a negative charge but not positive charge in between them. Thus to keep system of three charges in equilibrium, we need to keep two positive charges at the ends and a negative charge in between. We need to write the conditions  for zero resultant force location in at least on two charges so that we can get the magnitude,location and nature of the charge in between to get the answer as shown in the video lesson below.
 

Finding separation between two charges suspended from rigid support

Let us consider two identical ball of same mass and similar charge kept suspended from a rigid support using a light wire and because of the repulsion there will be some angular as well as physical separation between them. We need to find that angular separation in terms of the given data and the video solution is as shown below.

Motion of Charged particle in Electric Field

Let us consider a charged particle is moving horizontally with some constant velocity and an electric field is applied perpendicular to the motion. Gravitational force is small and we can ignore it in this case. Thus there is no force in the horizontal direction and hence the charged particle will have constant velocity over the horizontal direction. 

There is no initial velocity along the vertical direction but there is electric force due to intensity along the Y axis. Thus the particle experience acceleration along Y axis and hence the velocity of the particle increases on that axis. We can find the final velocity along each direction and its displacement along both the axes. It is further shown in the video lesson that the path of the charged particle is parabola as shown below.


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Electric force and Coulomb's Inverse square law Video Lesson

Electric force of attraction or repulsion exists between every two charges and it follows Coulomb's inverse square law. According to the law, the force between two charges is directly proportional to the product of charges and is inversely proportional to the square of the distance of separation.

Gravitational and electric forces are fundamental in nature. Gravitational force is due to mass of the particle and it exits between every two masses where as electric force exits between the the particles or bodies having only excess charges. Both of them obeys inverse square law but gravitational force is independent of medium but electric force depends on the medium between charges.

Gravitational force is the weakest of fundamental forces but electric force is much stronger than that. Gravitational force is further always attractive force but electric force is either attractive or repulsive. Further classification is explained in the video lesson below.


Coulomb's inverse square law

To identify the relation between the force and charges different experiments were conducted and we got to a conclusion that the electric force between the charges is directly proportional to the product of charges and is inversely proportional to the square of the distance of the separation.  The force also depends on the medium between the charges and its impact is studied basing on the permitivity of the medium. The ratio of permitivity of the medium to the permitivity of the free space is called dielectric constant or relative permitivity. Its value for the vacuum is one and for any non conducting medium it is greater than one. It is explained as shown in the video lesson below.



Effect of the medium on force between the charges

As we have explained earlier, we can understand that the force between the charges gets reduced when the medium is placed instead of the vacuum. It is further explained in the video lesson below. We can find out the effective distance in the presence of medium as shown below.



Impact of force between two charges when third charge is placed 

Electric force between the charges is not effected even if we keep a new charge in between them. What makes a difference is, more forces are acting on each  charge and hence resultant force on each charge is more. But the force between two charges is not affected because of the third charge. To find the resultant charge, we can use vector laws of addition. It is explained in the video lesson below.


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Properties of Electric Charges Video Lesson

Electric charge is the property of a particle of certain mass due to which it can either attract the opposite charge or repel the similar charge.Charges are classified as positive and negative and many bodies around  are neutral which means they have equal and opposite charges. 

When one body with excess charges is rubbed with the other, there is transfer of electrons from one body to other. The body lost electrons will have excess positive charges and the body that gained electrons will have excess electrons. Thus the body that gained electrons is negatively charged and the body that lost electrons is positively charged.

Thus body that is positively charged losses a small portion of mass due to loss of electrons and the body  that gained electrons is not only negatively charged but its mass is also  slightly increases.



Properties of Charges

Similar charges repel each other and opposite charges attract each other. This force of attraction obeys inverse square law. According to it the force of attraction or repulsion is inversely proportional to the square of distance of separation. It is a long distance range force. Further properties are explained in the video lesson below.


Number of electrons in one coulomb charge

We know that electron is treated like a fundamental charge and it is measured in a unit called coulomb. We also know that the charge is always available as integral multiples of charge of electron and this concept is called quantization of the charge. Taking that concept into consideration, we can find the number of electrons in one coulomb charge as shown in the video lesson below.



Methods of electric charging

We can charge the body by rubbing one body with the other. This is called charging a body by friction and during the rubbing, one body loose the electrons and the other body gains the electrons. We can also charge a body by conducting where we are passing the charge through the materials which has the ability to pass the current. We can also charge a body by keeping the body in contact. In that case excess charges from one body to other get transferred until there is some potential difference between them. It is explained in the following video lesson.

Charging a body by induction

Induction is the phenomenon of rearrangement of charges in a neutral body in the presence of a charged body. This separation of charges is called polarisation of charges and we can get a body charged using induction method with out getting in touch and contact with the body. It is explained in the following video lesson below.



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Electromagnetism Complete Lesson

Electromagnetism is a branch of physics that deals with the magnetic field developed around the current carrying conductor or moving charge. To find the magnitude of the magnetic field induction, we can use Biot-Servert's law and ampere's law. We can define the fundamental unit to measure the current ampere basing on this definitions. We can also measure force between two straight conductors. As mentioned in the posts in the relevant topics, we can find magnetic induction for different kind of current carrying conductors using these rules.

If a current carrying conductor is placed under the magnetic field, it experience two magnetic fields and because of them, there is torque experienced by the current carrying conductor and we can design moving coil galvanometer basing on this concept. It can be even converted into Ammeter and voltmeter. All these are discussed in detail in the following posts.

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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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Amepere's Law and Magnetic Field around Conductor

We can also find out the magnetic field induction at any point due to a charge using the Ampere’s law.According to this rule the line integral of magnetic induction around a closed curve is permittivity of free space times the current in that closed loop.


Problem and solution

Let us consider a current carrying conductor in circular shape and we are interested in the magnetic field at the center of the coil. We can use the formula that we have derived to do that and we shall assume that the distance of the particle on the perpendicular axis is zero. It is because we are measuring it at the center of the coil. The problem is solved as shown below.



When we measure the line integral, we get the length of the wire around which we are measuring the magnetic field. We also need to measure the magnetic field only due to currents inside the closed loop. We need not worry about the currents outside as they do not produce any impact. We are measuring only due to the portion of currents that are in the closed loop.

The currents with in the loop which are coming into the loop are treated as positive and currents leaving the closed circuit shall be treated as negative.



Basing on this Ampere’s law, we can find the magnetic field around a closed straight current carrying conductor of infinite length as shown below.

Let us assume a conductor carrying a current “I” as shown in the figure. We would like to measure the magnetic field around it at a distance “r” from it.  We can consider the line integral around it as the circular path of the given radius and when we line integrate it; we get the length of that closed path. It is nothing but the circumference of the circle.



It is the dot product of the magnetic field and the component of the length due to which we need to measure the field as per the Amper’s law. Any way the field and the portion of the length are in the same direction and the angle is treated as zero.

In the place of that line integral of the component of the length, we need to write the circumference as shown and we can find the magnetic field as shown below.



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Current Electricity Complete Lesson

Current electricity is a branch of physics that deals with the charges in motion and its applications. Current flows through the conductors and while it is happening some opposition is there called resistance. In this lesson we have analyzed on whom this resistance is depending on and how can we measure it. To measure the nature of resistance and its dependence, a physical quantity called specific resistance is also defined. It depends on the nature but not on the physical dimensions of a body. 

To know the dependence of the current on potential difference in simple cases, Ohm's law is defined and to study the complex cases, we have Kirchhoff's laws. To know about the impact of resistance, we have Wheatstone bridge and its application Meter bridge. We also deal here about potentiometer and it is useful to compare the EMF of different cells and to find the internal resistance of a battery. Detailed lessons were made about each of the above topics and they are listed here for the reference.

Resistance and Specific Resistance

EMF and Internal Resistance of a Cell

Kirchhoff's Laws and Explanation

Kirchhoff's Law Problems and Solutions

Wheatstone bridge and Meter Bridge

Potentioemeter Comparison of EMF's and Determination of Internal Resistance

Resistors in Series and Parallel Problems and Solutions


Other complete lessons in this blog are mentioned here for the reference.

Gravitation Complete Lesson

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