The calculation of E Due to a Point Charge is very crucial in various numerical in Physics. However, before going deep into the calculations and derivations, you must understand the concept behind them.
In the following paragraphs, you will get to know what Electric Field Due to Point charge is and how you can derive its calculation.
What Are Electric Fields Due To Point Charge?
The basic property of any matter is that it has an electric charge. The electric charge regulates the working of the electric field or the magnetic field, which affects the fundamental particles around a particular body. The space around an electric charge in which their effect can be felt is called the electric field.
You can comprehend the capacity of a charge to control any other charges in any space by considering the strength of that charge in its electric or magnetic field. The force exerted by a charged particle in its electric field is called electrostatic force. The charged particle exerts this force on the other charges present in the field. The electric field is a vector quantity.
You can easily measure the electric field intensity by considering the force exerted by a point charge on a unit charge. Therefore, you can say that the electric field is defined as the force per unit charge.
Concept Of Electric Field
The interaction between any two objects can be explained through the mutual forces exerted due to the charges of the atoms and molecules, attracting each other in close space. In this way, a field is produced at a distance and without any physical contact, in which the objects are likely to attract one another.
When the two objects of like charges are placed together, they repel each other. Whereas the two objects with unlike charges attract one another. The electric field is denoted by E, and its unit is NC-1 or Vm-1.
- When a rubber comb is charged, it attracts plane bits of paper placed near it because of the Coulomb force produced around them. This force creates an electric field around them, and this field carries the force, which attracts the bits of paper. That is why bits of paper get attracted from a distance, without any physical contact.
- The gravitational field surrounds Earth, and if any other mass comes within its field, it will also experience the earth’s gravitational force. Similarly, in our daily life, we witness several objects exposed to electric fields, such as the field produced by electric motors, radio transmitters and mobile phones.
Characteristics Of Electric Field Lines
Michael Faraday was the first who drew electric field lines and made us aware of their properties. These field lines are drawn by drawing tangents from the position of charge, and therefore the direction of the electric field at that point is the same as the tangent to the electric field.
However, some features are unique to electric field lines, and whenever you draw an electric field line, you should keep these points in mind.
- The direction of the field line is always perpendicular to the charge’s surface.
- Two electric field lines can never intersect at any point.
- The number of field lines emerging from a point is indicative of the strength of the electric field at the point, i.e., the magnitude of charge.
- Electric fields should always arise from the positive charge and terminate at a negative charge.
- When the electric field lines of a single charge or point charge are drawn, the magnetic field lines start or terminate at infinity.
Formula And Derivation Of Electric Field Generated By Point Charge
The electric field formula is Fq, where F is the Coulomb per electrostatic force exerted on a positive point charge q. And the magnitude of the electric field created due to point charge q is E = k|q|r2, where r is the distance from q.
Moreover, you can detect the electric field of charge q by considering a test charge q0 and then measuring the force that acts on it.
So, the force exerted per unit charge is
The test charge q has the capacity to exert an electric field, and thus to prevent the effect of the test charge; you should reduce its charge. Therefore, the magnitude of electric charge is
This shows the electric field of a point charge q. In some cases, when the charge q is positive, E is the direction in which force F acts. In such cases, acceleration is A = F/m = QE/m. and when the charge is negative, then the force acts in the opposite direction of E. In this case, acceleration is negative, i.e, A = F/m = – QE/m.
However, the charge in the electric field produced is influenced by force irrespective of its position. An electric force is dependent on the charge of the object, but it is independent of its mass and velocity.
System Of Point Charge
When an electric field is produced due to a system or chain of charges at any point, the intensity of the electric field becomes the vector sum of the electric field caused by all the charges at the same point.
Do not worry if you don’t know how to find the vector sum of electric field intensity. Let’s discuss it here.
Here, rn indicates the distance of the point from the nth charge denoted by qn. ^ris the unit vector in this equation.
Let’s assume that these charges, i.e., q1,q2̣….qn, are placed in a vacuum at placed indicated by vector r 1r2…… rn. Therefore, the net force will be calculated as follows:
The obtained equation is used to calculate the electric field formed by a system of point charges.
Electric field due to a point charge is calculated using the expression mentioned above. However, the calculation for two or more point charges in a plane is completely different but not too complex; you just need to summate all the values. Moreover, while drawing the field lines of a point charge, you should never break the rules set by Faraday about the properties of field lines.
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