Showing posts with label Electric Field. Show all posts
Showing posts with label Electric Field. 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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Resultant Force and Coloumb's Law of Electric Force Problems and Solutions
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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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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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Magnetic Field due to Current Carrying Conductor

In the beginning electricity and magnetism were treated like different subjects. People could not find any relation between them. Electricity is found to be due to the charges and magnetism is thought to be due to the different poles like north and south poles. The force between them and treatment of each subject is done quite separately and they do exist like to separate branches of physics.

In the earlier days of nineteenth century some experiments done by famous scientists found that with the change in the electric field, there is magnetic field also developed around it. This leads to new science called electromagnetism.

The experiments found that the charged particle in the state of rest gives electric field around it. If the charge is moving or if there is a flow of current in any conductor, around it there is not only electric field and there is also a magnetic field.

It can be noticed that the magnetic needle with north and south poles will keep on changing its direction around a electric charge as shown in the diagram.



We can find the direction of the magnetic field using different laws. One of those kinds of rule is Maxwell’s cork screw rule. If there is a nail that rotates using the right hand and if we rotate the screw in such a way that the nail advances in the direction of the current, the direction of the magnetic field is along the direction of the rotation of the head of the nail. It can be understood that the rotation of the head of the nail and the tip of the nail are in the perpendicular plane. Thus electric and magnetic fields are in the perpendicular plane.


We can also use a rule called right hand thumb rule to identify the direction of the magnetic field. It is somehow similar to cork screw rule. If we hold a current carrying conductor with our hand such that the thumb is along the direction of the current, the direction of the magnetic field is along the direction of the curled fingers. It again tells you that the electric field and the magnetic field are in the perpendicular planes.


Around every magnetic pole, there is some space up to where its influence can be experienced. That space is called magnetic field. If we keep any other magnetic pole with in that field, it experiences a force of attraction or repulsion. That force is called magnetic field induction. We can define the magnetic field induction as the force experienced by a unit North Pole placed in the magnetic field.

Around every current carrying conductor, there is a magnetic field and there is a magnetic field induction. To measure that value we have different rules and one among them is Biot-Servert’s law. According to this rule, the magnetic induction at any point directly proportional to the some factors like the  SIN angle it makes with the point, current passing in the conductor, component of the part of the length of the portion of the wire due to which we are measuring the magnetic field and is inversely proportional to the square of the distance of separation.




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Current Electricity Complete Lesson

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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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Electrostatics Complete Lesson

Electrostatics is a branch of physics that deals with charges in the state of rest and its applications. Here in this chapter we are going to deal about charge, electric field, electric force between charges,electric intensity,electric potential,potential difference, electric potential energy,capacitor, capacity, effect of dielectric on the capacity and energy stored in capacitor etc. Detailed lessons are made about each of the topic and they are listed here below for the reference.

Electric Charge and Electric Force


Resultant Force and Coloumb's Law of Electric Force Problems and Solutions

Here are the further list of topics with complete lessons in this website.

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Capacitors in Series and parallel with Problems and Solutions

Capacitor is a device that is capable of storing energy and charge between its plates. We can connect the capacitors in different combinations.

Capacitors in Series

If one plate of the capacitor is connected to the other charged plate to the next capacitor and keep on connecting, this kind of connection is called series connection, When they are connected in series, the charge distribution on all of them is same but the total voltage connected to the system is shared across different capacitors basing on their capacity.

In series combination, total voltage of the system is the sum of all voltages shared across the system. We can find that the effective capacity of capacitors is less than any individual capacitors. It can be derived as shown below.



 Capacitors in Parallel

When capacitors are connected in parallel, the voltage shared across each capacitor is similar to the individual voltage on each capacitor. But the charge supplied to the system is shared across different capacitors based on their capacities.

If all positive plates of different capacitors are connected together and the negative plates of capacitors are also connected together, this kind of combination is called parallel combination.


When capacitors are connected they together can acquire a common potential as shown below. If different kind of plates are connected, the answer vary with the sign.


Problem and Solution

We know that when capacitors are connected in series, the effective capacity decreases and when they are connected in parallel, their effective capacity increases. If individual capacitors were need to be find out basing on total capacity of the systems when they are connected in series and parallel, we can find as shown in the problem below.


Problem and Solutions

When capacitors are connected in series, the charge across all the capacitors is same, but voltage is shared across them. We can find individual voltage as show in the diagram and problem with solution below.



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Electric Charge and Electric Force
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Resultant Force and Coloumb's Law of Electric Force Problems and Solutions

Electric charges apply force of repulsion on similar type of charges and apply force of attraction on opposite kind of charges. The magnitude of the force of attraction or repulsion  can be measured using Coloumb's Law of force.

If there are multiple force acting on a charge due to multiple charges, we need to use vector laws of addition to identify the resultant of all the forces. We can use parallogram law and triangle law of vectors to find the resultant of the total force acting on the system.

If three identical charges are at three corners of the triangle, the resultant force on a charge at the centroid of the triangle is zero as three force acting on it behaves like three force of triangle law and hence their resultant force is zero.

It can be further shown that if one charge at any corner is different in nature, resultant at the center is not going to be zero as the forces are not going to cancel out. We can find the resultant as shown below.


The case is same when four identical charges are placed at the four corners of the square. The resultant force on the fifth charge placed at the cross section of the diagonals is zero. If the charges change their nature, the effective force will be different.


Resultant force due to multiple charges

Let us consider two similar charges at the two corners of equilateral triangle and we would like to measure the resultant force at the third corner of the triangle. The two forces acting on the third charge are equal in magnitude but having some angle between them. To find the resultant force, we need to use parallogram law of vectors.



We can repeat the same and solve the problem, when the charges are in opposite nature but the resultant is different from the earlier case. The reason is though the forces are same like the previous case, they do act in opposite directions and hence the resultant force is different.


Let us assume a scenario where four identical charges are placed at the four corners of the square and we need to measure the resultant force on any charge that is at the any corner of the square. On the forth charge, there are three force acting due to three charges. Forces due to two charges are equal in magnitude and they are perpendicular to each other. Their resultant is along the direction of the third force due to the third charge. We need to use parallogram law to find the total force acting on it. It is as solved below.


We can also find the magnitude of the charge that has to placed at the cross section of the diagonals, so that the entire system is in equilibrium.


We can solve a problem where good number of charges are placed on the x axis from a initial point and we need to measure what kind of charge that has to be placed at the origin so that the resultant force on it will be zero.


Let us consider identical charges places on horizontal axis as shown and the resultant force can be measured as shown below.


If we put different charges in contact, there will be flow of charge from one to other until equilibrium is reached. As charges are redistributed, the force between them will change once they are separated back to some distance of separation.

 Problem and Solution

 Let us consider two charges of different nature separated by a certain distance of separation.Now this two charges are got into contact and separated back  to a different distance. What is the new force between them ?

 Solution

 When two different charges are brought into contact, there will be flow of charge from one body to other until they get equilibrium. With the new charge distribution and with different distance of separation, new force between them can be measured once again using Coloumb's law of force as shown.

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Gravitational Force of Attraction and Newton's Law

Resultant Gravitational Force and Neutral Point
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